reconfigurable split ring resonators using pneumatics
TRANSCRIPT
Reconfigurable Split Ring Resonators using Pneumatics
A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy
Xutao Tang
B.Eng. (Hons), School of Engineering, RMIT University
School of Electrical and Computer Engineering
College of Science Engineering and Health
RMIT University
March 2017
Declaration
I certify that except where due acknowledgement has been made, the work is that of the author alone;
the work has not been submitted previously, in whole or in part, to qualify for any other academic
award; the content of the thesis is the result of work which has been carried out since the official
commencement date of the approved research program; any editorial work, paid or unpaid, carried
out by a third party is acknowledged; and, ethics procedures and guidelines have been followed.
I acknowledge the support I have received for my research through the provision of an Australian
Government Research Training Program Scholarship.
Xutao Tang
1 March 2017
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ACKNOWLEDGEMENTS
The completion of this thesis is impossible without the valuable help from many people. I
would like to express my sincere gratitude to my senior supervisor Associate Professor
Wayne Rowe for his extraordinary patience, consistent encouragement and valuable advice
throughout the entire duration of my Ph.D. candidature. It is his encouragement that helps me
to overcome the most difficult time in research. Without his support, the thesis could not be
the present form. I would also like to thank my secondary supervisor Dr. Iryna Khodasevych
who, with exceptional knowledge in resonators, gives me great help in achieving this thesis.
My gratitude also goes to my secondary supervisor Dr. Jiao Lin for his kindly and
encouraging suggestions. I would also like to express my appreciation to Professor Arnan
Mitchell for his valuable suggestions during the planning and development of this research.
I would also like to thank my colleagues Dr. Thomas Baum, Dr. Francisco J, Dr. Mahyar
Nasabi, Mr. Jiuyang Zhu, Dr. Negin Shariati Moghadam, Mr. Paul Jones, Mr. Chris Arthur,
Ms. Chiping Wu and other, who always gives= me helpful advice and encourage me during
the Ph.D. research. My huge gratitude goes to Mr. Yuxun Cao and Mr. Alexander Zylewicz
for their exceptional technical skills.
A key person whom I am particularly indebted to is Mr. David Welch, the technician in
School of Engineering. He is always happy to spend time discussing practical sections with
me about my work. His outstanding technical skills and practical advice gave me the most
invaluable help in the realisation of this thesis.
I would like to thank RMIT University for the financial support to my research and providing
equipment and facilities, which is critical for the completion of my thesis.
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Finally, I wish to thank my beloved parents, for their support both emotionally and
financially. I would also like to thank my little brother, Saber Tang, who is always cheerful
and proud of his brother, which motivates me so much towards the finish of my Ph.D. For my
lovely fiancée, Qinghua Mou, I could not express how deep my gratitude to you. Because of
you, there will never be an obstruction I cannot overcome; there will never be a challenge I
cannot defeat, there will never be a worry that lasts more than a day. Thank you.
Last but not the least I would like to thank everybody who has been involved directly or
indirectly in the successful completion of my research. To all, thank you so much!
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Table of Contents
ACKNOWLEDGEMENTS ..................................................................................................... iii
Table of Contents ....................................................................................................................... v
List of Figures ........................................................................................................................... ix
List of Tables .......................................................................................................................... xiv
Abbreviations and Acronyms .................................................................................................. xv
Abstract ...................................................................................................................................... 1
CHAPTER 1 .............................................................................................................................. 4
Introduction ................................................................................................................................ 4
1.1 Introduction .................................................................................................................. 4
1.2 Problem Statement ....................................................................................................... 5
1.3 Motivation .................................................................................................................... 6
1.4 Objectives .................................................................................................................... 6
1.5 Scope ............................................................................................................................ 7
1.6 Thesis structure ............................................................................................................ 7
1.7 List of publications ...................................................................................................... 9
1.8 Original Contribution ................................................................................................. 10
CHAPTER 2 ............................................................................................................................ 11
Background and Literature Review ......................................................................................... 11
2.1 Introduction ................................................................................................................ 11
2.2 Split Ring Resonators ................................................................................................ 12
2.2.1 Background and Theory .................................................................................. 12
2.2.2 Field Orientation ............................................................................................. 15
2.2.3 Split Ring Resonator Coupling ....................................................................... 16
2.3 RF devices incorporating SRRs ................................................................................. 19
2.4 Reconfigurable resonator structures .......................................................................... 20
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2.5 Reconfiguration Mechanisms .................................................................................... 20
2.5.1 External Components ...................................................................................... 20
2.5.2 Microfluidic/Pneumatic modification ............................................................. 25
2.6 Summary .................................................................................................................... 28
CHAPTER 3 ............................................................................................................................ 30
Dynamic resonator tuning by pneumatic levitation ................................................................. 30
3.1 Introduction ................................................................................................................ 30
3.2 Design of the split ring resonator ............................................................................... 32
3.3 Pneumatic levitation structure.................................................................................... 34
3.3.1 Design Concept ............................................................................................... 34
3.3.2 Fluid simulation .............................................................................................. 35
3.3.3 Assembly of the pneumatic levitation system ................................................ 38
3.3.4 Prototype fabrication ....................................................................................... 40
3.3.5 Experimental confirmation of the levitation ................................................... 40
3.4. Dynamic tuning of split ring resonator ..................................................................... 44
3.4.1 Design of levitation platform .......................................................................... 44
3.4.2 Simulation ....................................................................................................... 45
3.4.3 Experimental setup and mechanical measurement ......................................... 49
3.4.4 Measurement ................................................................................................... 50
3.5 Summary .................................................................................................................... 55
CHAPTER 4 ............................................................................................................................ 56
Pneumatic levitation reconfigurable coupled split ring resonators .......................................... 56
4.1 Introduction ................................................................................................................ 56
4.2 Pneumatic system design ........................................................................................... 57
4.2.1 Design Concept ............................................................................................... 57
4.2.2 Assembly of the structure ............................................................................... 57
4.2.3 Principle of system operation.......................................................................... 59
4.2.4 Fabrication of the structure ............................................................................. 61
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4.3 Parameter range validation ........................................................................................ 61
4.4 Split ring resonator design ......................................................................................... 65
4.5 Simulation and measurement ..................................................................................... 66
4.6 Reconfiguration results .............................................................................................. 70
4.7 Equalising frequency step .......................................................................................... 75
4.7.1 Structure alteration .......................................................................................... 75
4.7.2 Results verification ......................................................................................... 76
4.8 Summary .................................................................................................................... 80
CHAPTER 5 ............................................................................................................................ 81
Lateral control of SRRs using pneumatics............................................................................... 81
5.1 Introduction ................................................................................................................ 81
5.2 Lateral control of SRRs ............................................................................................. 82
5.2.1 Operational concept ........................................................................................ 82
5.2.2 Pneumatic lateral control structure ................................................................. 84
5.2.3 Air restrictor layer ........................................................................................... 87
5.2.4 Coupled Split Ring Resonators ....................................................................... 89
5.2.5 Simulation ....................................................................................................... 90
5.2.6 Experimental Set-up and Measurements ........................................................ 92
5.3 Reconfigurable CPW filter ........................................................................................ 94
5.3.1 Introduction ..................................................................................................... 94
5.3.2 Structure and Simulation................................................................................. 95
5.3.3 Measurement ................................................................................................... 97
5.3.4 Coupled SRRs loaded CPW filter ................................................................. 100
5.3.5 Measurement ................................................................................................. 102
5.4 Reconfigurable Antenna using SRRs....................................................................... 103
5.4.1 Introduction ................................................................................................... 103
5.4.2 Structure and Simulation............................................................................... 104
5.4.3 Experimental results...................................................................................... 111
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5.5 Summary .................................................................................................................. 114
CHAPTER 6 .......................................................................................................................... 115
Thesis Summary..................................................................................................................... 115
6.1 Introduction .............................................................................................................. 115
6.2 Chapter 1 and 2 ........................................................................................................ 115
6.2 Chapter 3 .................................................................................................................. 116
6.3 Chapter 4 .................................................................................................................. 118
6.4 Chapter 5 .................................................................................................................. 120
References .............................................................................................................................. 124
ix
List of Figures
Figure 2.1: (a) Split ring resonator and (b) its equivalent L-C circuit. .................................... 12
Figure 2.2: The split ring resonator in electromagnetic field with different orientations. (a) the
gap is parallel to the E-field, (b) the gap is perpendicular to the E-field. ................................ 16
Figure 2.3: Different coupling modes of SRRs, (a) conventional edge coupled SRRs, (b)
modified edge coupled SRRs, (c) conventional broad-side coupled SRRs, (d) modified broad-
side coupled SRRs. .................................................................................................................. 18
Figure 2.4: Electrical components for reconfigurable SRRs (a) capacitor loaded [80], (b)
varactor-diode loaded [83], (c) photon-diode loaded [91]. ...................................................... 22
Figure 2.5: A reconfigurable SRR using MEMs switch (a) off and (b) on stage of MEMS
switch [104], (c) photograph of MEMS switch [101].............................................................. 23
Figure 2.6: Mechanical means of structure reconfiguration (a) motor driven rotation of SRR
[106], (b) stretchable SRR substrate [114]. ............................................................................. 24
Figure 2.7: Reconfigurable SRRs using Microfluidic channels [120]. .................................... 26
Figure 2.8: Reconfigurable SRRs using pneumatic actuation (a) pneumatic switch in off and
on stage [126], (b) behaviour of tunable SRR using pneumatic force [130] ........................... 27
Figure 3.1: Flowchart showing the methodology for this research. Sections in orange are not
discussed in this chapter........................................................................................................... 31
Figure 3.2: (a) Broad-side coupled SRRs structure and (b) the equivalent circuit .................. 33
Figure 3.3: Schematic of the levitation concept....................................................................... 34
Figure 3.4: Cross-section of the pneumatic levitation structure for fluid simulation. ............. 36
Figure 3.5: Fluid simulations showing the cross-section of the levitation structure ............... 38
x
(a) small dynamic pressure due to the large channel, (b) excessive dynamic pressure due to
tide channel, (c) low air flow velocity, (d) high air flow velocity, (e) turbulence level with the
large channel, (f) the turbulence level with small channel. ..................................................... 38
Figure. 3.6: (a) Layout of the levitation structure (b) the levitation platform ......................... 39
Figure 3.7: (a) Schematic of the experimental setup for levitation; (b) photograph of the
experimental setup. .................................................................................................................. 42
Figure 3.8: The photographs taken for the cross-section of the levitation structure (a) no
pneumatic pressure, (b) high pneumatic pressure. .................................................................. 43
Figure 3.9: Levitation heights with different amount of pneumatic pressure. ......................... 43
Figure 3.10: 3D rendering of the underside of various levitation platforms ........................... 45
Figure 3.11: Schematic of the broad-side coupled SRRs. ....................................................... 46
Figure 3.12: Simulation results of |S21| with different rotational angle θ in a single SRR ...... 47
Figure 3.13: Simulation results of |S21| with bottom SRR at 0 degrees and 2 mm from the top
SRR .......................................................................................................................................... 48
Figure 3.14: Simulation results of |S21| with bottom SRR at 90 degrees and 2 mm from the top
SRR .......................................................................................................................................... 48
Figure 3.15: Experimental setup .............................................................................................. 50
Figure 3.16: Measurement results for rotation of the top statically placed SRR ..................... 51
Fig. 3.17: |S21| for rotation angle θ statically from 0° to 180° and lower SRR at 0o ................ 52
Fig. 3.18: |S21| for rotation angle θ statically from 0° to 180° and lower SRR at 90o .............. 52
Figure 3.19: Spinning speed profile respond to pneumatic pressure ....................................... 53
Figure 4.1: Flowchart showing the methodology of this investigation. Sections in orange are
not discussed in this chapter. ................................................................................................... 56
Figure 4.2: Cross-section of the levitation module. a = 34 mm, b = 15 mm, c = 1 mm, e = 25
mm ........................................................................................................................................... 58
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Figure 4.3: (a) 3D rendering of the levitation platform and air floor: r1 = 31 mm, H1 = 1.7 mm,
h1 = 0.5 mm, t1 = 0.5 mm, r2 = 29 mm, H2 = 2.5 mm, h2 = 0.5 mm, h3 = 1 mm, t2 = 0.5 mm,
(b) operation of the levitation and spin mechanism ................................................................. 60
Figure 4.4: Photographic processing for levitation measurement due to different pneumatic
pressure .................................................................................................................................... 62
Figure 4.5: Levitation height vs applied pneumatic pressure .................................................. 63
Figure 4.6: Schematic of the broad-side coupled SRRs: r = 6mm, w = 0.6 mm, g = 0.5 mm, R
= 7 mm, t = 0.508 mm, s = separation between two rings with initial 0.5 mm value due to h2
in Fig. 4.2(a), θ = ring rotation angle. ...................................................................................... 65
Figure 4.7: Experimental set-up ............................................................................................... 66
Figure 4.8: Simulation model for examining the holes in the waveguide ............................... 67
Figure 4.9: Magnetic field distributions on the cross section of the waveguide along wave
propagation direction. (a) Field distribution on the conventional waveguide. (b) Field
distribution with holes on the waveguide. ............................................................................... 68
Figure 4.10: Electric field distribution of two broad-side coupled SRRs ................................ 69
(a) large separation (b) small separation .................................................................................. 69
Figure 4.11: Simulation result of the empty pneumatic structure in waveguide ..................... 70
Figure 4.12: |S21| values of coupled SRRs at different rotation angle with s = 0.5mm ........... 71
(a) Simulation results (b) Measurement ................................................................................... 71
Figure 4.13: |S21| with different separation s when rotation angle is θ = 0o ............................. 72
(a) Simulated (b) Measured ..................................................................................................... 72
Figure 4.15: Control mapping of the broad-side coupled SRRs using the pneumatic switching
.................................................................................................................................................. 74
Figure 4.16: |S21| tunability based on the angle θ between two rings when s = 0 mm for the
equalised frequency step structure (a) simulation (b) measurement ........................................ 76
xii
Figure 4.17: Simulated/Measured |S21| comparison at different rotation angles versus
separation (a)/(b) θ = 0o, (c)/(d) θ = 20o, (e)/(f) θ = 40o, (g)/(h) θ = 80o, (i)/(j) θ = 180o ........ 78
Figure 4.18: Control mapping of the broad-side coupled SRRs using the equalised frequency
step pneumatic switch .............................................................................................................. 79
Figure 5.1: Flowchart showing the methodology of this work. Sections in orange are not
discussed in this chapter........................................................................................................... 81
Figure 5.2: Conversion of coupling mode arrangement for SRRs........................................... 83
Figure 5.3: Edge-coupled SRRs (a) Configuration A, and L-C equivalent circuit (b)
Configuration B ....................................................................................................................... 83
Figure 5.4: The layout of the pneumatic levitation system. (a) The completely assembled
structure on the left and exploded view of the structure on the right. (b) Underside view of the
top layer. .................................................................................................................................. 85
Figure 5.5: (a) Orifice plate (b) Air flow simulation of the orifice plate ................................. 87
Figure 5.6: (a) Schematic of the coupled SRRs (b) representation of the coupling mode
transition .................................................................................................................................. 90
Figure 5.7: Simulation results for coupled SRRs with different displacement ....................... 91
(a) configuration A (b) configuration B ................................................................................... 91
Figure 5.8: Schematic of the experimental set-up ................................................................... 93
Figure 5.9: Measurement of |S21| for coupled SRRs with different displacement ................... 93
(a) configuration A (b) configuration B. .................................................................................. 93
Figure 5.10: Photograph of CPW: W1 = 14 mm, W2 = 3 mm, g0 =0 mm, L1 = 50 mm .......... 95
Figure 5.11 Diagram of the movement of the SRR relative to the CPW, distinguished by
separation d .............................................................................................................................. 96
Figure 5.12: Simulated |S21| of CPW filter using pneumatic controlled SRR. ........................ 96
Figure 5.13: Experimental set-up ............................................................................................. 98
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Figure 5.14: Measured |S21| of CPW using pneumatic controlled SRR ................................... 99
Figure 5.15: The field strength on the cross section of the CPW showing the coupling
between SRR and CPW. (a) electric field distribution with 1.5 mm separation between SRRs,
(b) electric field distribution with 1 mm separation between SRRs ...................................... 100
Figure 5.16: Diagram of operation for the coupled SRRs loaded CPW filter. ...................... 101
Figure 5.17: Simulation results with different distance d between the two SRRs ................ 101
(a) configuration A (b) configuration B ............................................................................... 101
Figure 5.18: |S21| of CPW filter with different distance d between two SRRs ...................... 103
(a) configuration A (b) configuration B ................................................................................ 103
Figure 5.19: Schematic of the CPW-fed monopole antenna tuned by a SRR. ...................... 105
Figure 5.20: Simulation results of the reconfigurable CPW-fed monopole antenna (a) |S11| (b)
radiation pattern in z-y and z- x plane without structure reconfiguration. ............................. 106
Figure 5.21: Radiation pattern in x-y plane at 3.64 GHz with s = 0 mm. .............................. 107
Figure 5.22: Radiation pattern and surface current distribution at: (a) 3.5 GHz, s = -3 mm, (b)
3.5 GHz, s = 3 mm, (c) 3.77 GHz s = -3 mm, (d) 3.77 GHz s = 3 mm ................................. 108
Figure 5.23: Radiation pattern in different values of s (mm) ................................................ 109
(a) at the lower resonant frequency (b) at the higher resonant frequency. ............................ 109
Figure 5.24: Radiation pattern at 3.64 GHz ........................................................................... 110
Figure 5.25: |S11| parameter of a monopole antenna with different placement of SRR. ........ 111
Figure 5.26: Measured Radiation pattern at a different s with associated frequency. ........... 112
Figure 5.27: Radiation pattern at fixed frequency (3.5 GHz) ................................................ 113
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List of Tables
Table 2.1: Summary of conventional frequency reconfiguration technique............................ 29
Table 3.1: Summary of the simulated and measured resonant frequencies ............................. 51
Table 3.2: Resonant frequencies for broad-side coupled SRRs with lower SRR at 0 degrees.
.................................................................................................................................................. 52
Table 3.3: Resonant frequencies for broad-side coupled SRRs with lower SRR at 90 degrees.
.................................................................................................................................................. 53
Table 4.1: Summary of the tuning range at different rotation angles. ..................................... 74
Table 5.1: Frequency bands of the CPW-fed monopole antenna with different s ................. 107
xv
Abbreviations and Acronyms
RF Radio-Frequency
SRR Split Ring Resonator
DC Direct Current
MEMS Micro Electro Mechanical System
CPW Coplanar Waveguide
DSRR Double Split Ring Resonator
HFSS High Frequency Structural Simulator
|S21| Forward Transmission Coefficient
|S11| Reflection Coefficient
PMMA Polymethyl Methacrylate
DSLR Digital Single-lens Reflex Camera
ABS Acrylonitrile Butadiene Styrene
UHMW Ultra-high Molecular Weight
E-field Electric Field
1
Abstract
During the past decades, the rapid development of communication systems has extended to
every aspect of modern technology. To better satisfy the need of people to interact with the
world, investigations into the critical communication components mostly within the Radio-
Frequency (RF) range have faced a diverse range of operational requirements and
environment. The development of reconfigurable devices conforms to these demands with
broader applicability. The resonant circuit, consisting of an inductance and capacitance, is
fundamental to the design of passive resonant devices. The adjustment of their inherent
inductance or capacitance provides a pathway for frequency reconfiguration.
The split ring resonator (SRR) is first introduced to generate negative permeability in
artificial materials. The physical geometry of a SRR features a gap in a broken conductive
ring, and is characterised as a compact sized resonant circuit due to the effective capacitance
and inductance occurring on the gap and ring respectively. The integration of SRRs to RF
devices has been widely explored, not just to enhance the performance but also enable
reconfiguration in some resonant devices. The concept of tuning the intrinsic capacitance or
inductance of the SRR has been realised by the addition of active devices such as diodes and
MEMS switches. However, interference to the electromagnetic properties due to the
additional components and their bias line networks, and tolerance control on the placement of
the controlling element is a serious concern. If tuning is required in array structures such as
metamaterials, component count, and bias issues are significantly elevated.
The aim of this research is to investigate and conceive pneumatic levitation systems as a
mean of changing the structural arrangement of SRRs to reconfigure their resonant frequency
or other parameters. Rotation, elevation and lateral movement of the SRRs are realised by
2
implementing pneumatic levitation, and the resulting changes in the transmission response
are characterised.
The resonant frequency of a SRR is dependent on the orientation of the incident
electromagnetic waves. Pneumatic levitation is firstly proposed to allow free rotation of a
SRR in the azimuthal plane resulting in continuous resonant frequency variations. The
inclusion of another identical SRR located below the spinning SRR forms a broad-side
coupled architecture. Depending on whether the static SRR is placed parallel or
perpendicular to the electric field, the coupled SRRs can achieve 10% (2.66GHz to 2.39 GHz)
or 12% (2.67 GHz to 2.38 GHz) continuous frequency sweep respectively. The levitation
platform which holds the SRR is demonstrated to provide different spinning speed profiles
and hence frequency sweep rates for the SRR response based on various platform designs.
An advanced pneumatic levitation system is devised to allow discrete on-demand resonant
frequency control of broad-side coupled SRRs utilizing the rotation angle and separation of
SRRs. The pneumatic structure stops the upper SRR at desired locations to achieve an
associated resonant frequency response. The coupled SRRs can realise a 35% tunable
frequency range (3.236 GHz to 2.11 GHz) over 180 degrees of rotation. The separation of
SRRs, driven by the applied pneumatic pressure, demonstrates a tunable frequency range
from 0.7% to 11.3% depending on the set rotation angle.
The horizontal arrangement of SRRs introduces another dimension for structure tuning based
on the lateral space between two resonators. A pneumatic levitation system which enables
the manipulation of the horizontal placement of a SRR leads to a smooth conversion between
edge coupled and broad-side coupled SRRs. The transition affects the mutual capacitance of
the structure resulting in changes to the transmission response. A 28% frequency reduction
from 3.2 GHz results during the transition from edge coupled to broad-side coupled mode if
3
two gaps of the SRRs are initially facing each other. When the gaps are facing outwards at
the start, a second resonant frequency appears in the examined band and mirrors the shift of
the first resonance in the opposite direction, increasing from 3.2 GHz. The investigation of
the lateral control of a SRR using pneumatic levitation is further explored with the integration
of an SRR with a CPW and monopole antenna for proof of concept reconfigurable RF device
functionality.
The integration of pneumatic systems as an approach to tune the structure of SRRs exhibits
tremendous potential for the physical modification of coupled SRRs, and possibly also any
small resonant devices or components. Both simulation and experiments has demonstrated
the possibilities to manipulate frequency shift between 2.1 GHz to 3.24 GHz. Furthermore its
key advantages are its non-metallic structure which has minimal impact on the resonant
properties and incident field, the near frictionless operation, and the control over the degrees
of freedom of structural variation.
4
CHAPTER 1
Introduction
1.1 Introduction
Today’s communication systems are an essential part of modern technology enabling people
to interact. Investigations into critical communication components including antennas, filters,
and oscillators are demanded to push the limits of the communication systems. An
abundance of applications fall under the banner of Radio-Frequency (RF) communications,
ranging from 3 kHz to 300 GHz. The requirement of RF devices to operate with distinct
specifications in all operational environments demands the development of reconfigurable
structures that can tune (or re-tune) frequency, polarization or radiation pattern. Research into
approaches to enable reconfiguration of passive devices has become a trend.
The response of a resonant circuit, consisting of an inductance and capacitance, reaches its
maximum when applying an alternating current at the resonant frequency. Therefore, a
foundation for passive resonant devices to achieve reconfigurable resonant frequency is to
alter either their inherent inductance or capacitance. The split ring resonator (SRR) is first
introduced to provide a magnetic resonance in metamaterial applications to realise double
negative properties and other phenomena unseen in natural materials[1]. The SRR is a
compact sized (normally sub-wavelength) resonant circuit, in which the physical
characteristics (the split and conductive ring) are considered as the capacitance and
inductance. Due to its physical size and sharp response, it has become one of the most
common elements to conduct reconfiguration in resonant RF devices.
5
The concept of frequency reconfiguration or tuning is most commonly realised in the
available literature by using active devices to adjust the intrinsic capacitance or inductance of
the SRR. Standard approaches include connecting the split of SRR via a capacitor or re-
routing a partial section of the SRR via micro-electro-mechanical system (MEMS) switches.
Although the incorporation of the active devices has the capability to tune the resonant
frequency of the SRR, it is also evident that electromagnetic interference occurs because of
the additional electronic component and its associated bias network. There are also other
issues such as the misalignment of controlling layers in the MEMS switches scenario, and
component count in reconfigurable arrays, networks, or metamaterial architectures.
In this thesis, a novel reconfiguration approach based on pneumatic levitation is investigated
and applied to the frequency reconfiguration of SRRs.
1.2 Problem Statement
Conventional methods to enable reconfiguration of SRRs often require extra metallic
components to adjust the intrinsic capacitance or inductance of the SRRs. Electromagnetic
interference and other implementation/fabrication issues are unavoidable because of the
additional biasing structure. A detailed analysis of all existing reconfiguration methods will
be discussed in Section 2.4. The challenge is to create a means of reconfiguration that does
not impact the electromagnetic response of the SRR.
6
1.3 Motivation
The motivation of this research is to investigate pneumatic levitation systems as a new
method to conduct structural reconfiguration of SRRs. The manipulation of pneumatic force
promises to eliminate the common issues in conventional approaches including
electromagnetic interference from metallic bias networks, misalignment, and uncertainty in
tuning degrees of freedom.
1.4 Objectives
This study embarks on the following objectives:
1. To investigate and realise a pneumatic levitation system for the purpose of structural
reconfiguration of resonators to achieve frequency tunability.
2. To explore the influence of the pneumatic levitation system on the frequency response of
split ring resonators undergoing structural arrangement.
3. To expand the control of the SRRs over multiple dimensions in order to achieve exotic
frequency reconfigurability.
4. To incorporate the pneumatic levitation controlled SRRs into fundamental RF device
prototypes for the purpose of post-fabrication transmission modification and antenna
pattern reconfiguration.
7
1.5 Scope
The research in this thesis aims to deliver a fundamental investigation of pneumatically
controlled SRRs as an underlying technique for the reconfiguration of RF devices. Proof of
concept structures will be examined in order to highlight the novelty of the reconfiguration
technique, and its potential as a method of reconfiguration for resonant components and
networks. The development of an RF device for a specific application using this new
technique is beyond the scope of this research but could be a topic of future work.
1.6 Thesis structure
There are six chapters in this thesis dedicated to the investigation of pneumatically levitated
SRRs to enable reconfigurability.
Chapter 2: This chapter presents the background of the SRR element and a study of
individual SRR structures and coupled SRR systems. A comprehensive literature review of
research on reconfigurable approaches for resonant structures is also presented. The purpose
of this chapter is to explore the principle and benefits of the structural tuning of SRRs and
identify the critical issues in existing methods.
Chapter 3: This technical chapter investigates pneumatic levitation systems to govern the
arrangement of SRRs. A contactless platform controlled by pneumatic force is proposed to
continuously change the orientation of an individual SRR in an incident electromagnetic field.
A similar architecture also has the capability to control the relative rotational angle of broad-
side coupled SRRs, whilst limiting the variation of the structure to a single degree of freedom.
A continuous frequency sweep is observed due to the dynamic spinning behavior of the SRR.
8
The geometry of the pneumatic levitation system is also explored as a means of controlling
the spinning speed profile.
Chapter 4: A pneumatic levitation system that provides discrete frequency reconfiguration
in broad-side coupled SRRs is proposed. The levitation platform is investigated to be able to
stop at a specific position from a continuous spinning motion. Additionally, the pneumatic
pressure which provides the lifting force for levitation is utilised to provide adjustment to the
separation of broad-side coupled SRRs. Both the discrete orientation reconfiguration and the
separation of the broad-side coupled SRRs provide on-demand control over the resonant
frequency.
Chapter 5: A new dimension of structural tuning via pneumatic systems based on lateral
control is introduced. The layer-based pneumatic system directly manipulates the horizontal
placement of the SRRs to allow conversion between the edge coupled and broad-side coupled
mode of SRRs. The frequency is reconfigurable based on the lateral space between two
resonators. The utilization of lateral control is then applied to the investigation of SRR loaded
coplanar waveguides (CPWs) and a monopole antenna to demonstrate unique
reconfigurability.
Chapter 6: This chapter presents a summary of the thesis as well as proposing future
directions for the research.
9
1.7 List of publications
[C1] X. Tang, I. E. Khodasevych, and W. S. T. Rowe, "Tunable split ring resonators using air
pressure," 2016 IEEE 2nd Australian Microwave Symposium (AMS), 2016.
[J1] X. Tang, I. E. Khodasevych, and W. S. T. Rowe, "Dynamic control of a split ring
resonator via pneumatic levitation," Submitted to Electronics Letters.
[J2] X. Tang, I. E. Khodasevych, and W. S. T. Rowe, "Reconfigurable split ring resonators
using pneumatic levitation," Submitted to IEEE Transactions on Antennas and
Propagation.
[J3] X. Tang, Lin, J, and W. S. T. Rowe, "Lateral control of the coupling mode of SRRs
using pneumatics,” in preparation.
10
1.8 Original Contribution
This thesis contributes the novel concept of reconfigurable SRR using pneumatic levitation
techniques. The investigation into the arrangement of SRRs realised by the manipulation of
air exhibits exotic frequency shifting methods. The benefits of using pneumatic control are
also articulated. A summary of the contributions to the body of knowledge are listed below:
1. A novel pneumatic levitation system is proposed (Section 3.3), which can spin a SRR
(or other passive RF structure) in the azimuthal plane, resulting in continuous
resonant frequency variation. [J1]
2. Levitation platforms are introduced (Section 3.4) to provide a method of selection the
spinning speed profile of SRRs to achieve adjustable frequency sweep rates based on
the level of pneumatic pressure. [J1]
3. An advanced pneumatic levitation system (Section 4.2) allows discrete resonant
frequency control of broadside coupled SRRs. The rotational angle of a SRR relative
to a static SRR and the incident electromagnetic field can be set. [J2]
4. Regulation of the separation between a pair of broad-side coupled SRRs has been
demonstrated (Section 4.3), enabling discrete frequency variation dependant on the
amount of pneumatic pressure. [C1, J2]
5. The horizontal arrangement of SRRs is actuated by introducing pneumatic lateral
control (Section 5.2). The conveyor like movement of the SRR realises the dynamic
conversion between edge coupled and broad-side coupled SRRs to achieve a
reconfigurable frequency response. [J3]
11
CHAPTER 2
Background and Literature Review
2.1 Introduction
The electromagnetic device is one of, if not the most, important technologies in the modern
world. The development of electromagnetic devices has become an integral part of today’s
communication infrastructure. The foundation of classical electromagnetic theory dates back
to the 19th century when Maxwell’s theory predicted the existence of electromagnetic waves.
The effect of applying an alternating current to a circuit consisting of inductance and
capacitance shows a maximum response at the resonant frequency. Resonant circuits have
been widely used to design electromagnetic devices. In the RF domain, a variety of devices
such as antennas [2, 3], filters [4, 5], sensors [6, 7], and absorbers [8, 9] have drawn huge
attention, and their limits have constantly been advanced. The SRR is one of the latest family
members in resonant circuits, showing a strong presence in the design of RF devices due to
its sharp response, compact size, and potential for reconfigurability.
In this chapter, the theory of SRR and its associated coupled structures are reviewed. The
concept of reconfigurable RF devices is also discussed. Moreover, a comprehensive overview
of various approaches to enable reconfigurable SRRs is presented.
12
2.2 Split Ring Resonators
2.2.1 Background and Theory
The split ring resonator (SRR) was first introduced by Pendry [1] to realise a structure with
negative permeability, which provided experimental verification of an almost forgotten
concept of artificial materials known as the metamaterials [10, 11]. Metamaterials were
originally theorized by the Russian scientist Veselago [12] in 1968, showing unnatural
negative refractive index results from simultaneous negative values of permittivity and
permeability. Investigations into the SRR decades after the original concept of the
metamaterial was proposed are now not only limited to providing negative permeability. The
appearance of the SRR in a broad range of RF components has never stopped growing, due to
its small electrical size and sharp resonant response.
The SRR consists of a wire loop (or ring) with a broken gap (or split) in it. The SRR behaves
as a resonant circuit when excited with the electromagnetic field. The gap is acting as a
capacitive element, whilst the ring is acting as the inductive component [13-16].
(a) (b)
Figure 2.1: (a) Split ring resonator and (b) its equivalent L-C circuit.
13
In theory, the resonant frequency (𝑓0) of the SRR is generally represented by:
𝑓0 =1
2𝜋√𝐿𝐶 (2.1)
The value of the inductance (L) due to the metallic loop is calculated using:
𝐿 = 𝜇0𝜇𝑟𝑅𝑚(𝑙𝑜𝑔8𝑅𝑚
ℎ+𝑤−
1
2) (2.2)
Where 𝜇0 is the free space permeability, 𝜇𝑟 is the relative permeability of the substrate
material, 𝑅𝑚 = 𝑅 +𝑤
2, h is the height of the split ring, and w is the width of the metallic trace.
The values of the capacitance (C) attributed to the gap can be calculated using:
𝐶𝑔𝑎𝑝 = 𝜀𝑜𝜀𝑟(ℎ𝑤
𝑔+ (ℎ + 𝑤 + 𝑔)) (2.3)
Where 𝜀𝑜 is the free space permittivity, 𝜀𝑟 is the relative permittivity of the substrate material,
and g is the size of the gap.
In addition, the surface charge on the ring generates a voltage between two symmetric points
on the surface of the ring. Assuming the gap is much smaller than the perimeter of the
conductive ring, the capacitance due to the surface charge induced on the ring can be
expressed as [17]:
𝐶𝑠𝑢𝑟𝑓 =2𝜀𝑜𝜀𝑟(ℎ+𝑤)
𝜋𝑙𝑜𝑔
4𝑅
𝑔 (2.4)
The resonant frequency of the SRR only depends on the physical dimension of the metallic
ring and the electric/magnetic properties of the substrate materials. Based on this, many
approaches have been formed by researchers for the design of SRRs.
14
Investigations into the dependence of the frequency on the physical scale of the SRR have
been conducted. The radius/thickness of the ring and the radial and azimuthal gap [15, 18, 19]
have been demonstrated to modify the resonant frequency. In general, the radius of the ring
contributes to the intrinsic inductance of the SRR, therefore, larger radius would result lower
resonant frequency. On the other hand, the gap of the SRR directly determines the
capacitance of the SRR. A larger gap provides a smaller capacitance causing the resonant
frequency to drop. The width or thickness of the metal affects the inductance and capacitance
simultaneously. Increasing the bulkiness of the metal will decrease the mutual inductance and
capacitance. As a result, a thicker ring will have lower resonant frequency. Furthermore,
different shapes and numbers of rings have also been studied to alter the values of the
capacitance and inductance of the SRR structure [20-29]. For example, increasing the
number of rings and turns based on the conventional SRR effectively reduces the electrical
length of the structure, hence resonant frequency is reduced [22-24]. The quality factor (Q)
and operating of bandwidth is determined by the mutual inductance and capacitance of the
SRR, and are inversely proportional to each other. As the numbers of rings increases, the
inductance of the SRR decreases, but the capacitance of the SRR increases with higher rate.
Overall the quality factor Q of the SRR is expected to increase with larger numbers of SRR,
while bandwidth expected to decrease. The SRR structure has also been used to conceive a
defected ground structure known as the complementary split ring resonator (CSRR) [21, 26-
28]. It inherits the properties of original SRR, providing a negative permittivity at the
resonant frequency and producing a sharp band-stop effect while keeping an electrical small
size. Different shapes of SRRs to the traditional circular and square rings have also been
extensively studied [19, 25, 29].
The influence of electrical/magnetic properties of the substrate materials on the transmission
response of SRR is also a topic of study. In [30-32], a numerical study of the effect of
15
substrate properties on the SRR employs different materials with experimental verification of
adjustable relative permittivity 𝜀𝑟 and relative permeability 𝜇𝑟 . Given by the formulas
discussed in Section 2.2.1, the capacitance and inductance of SRR are directly proportional to
the permittivity and permeability respectively. The transmission response of the SRR can be
tailored by using different material or composites. Comprehensive analysis on different
design parameters of the SRR has also been undertaken [33, 34].
2.2.2 Field Orientation
Although the SRR was initially designed to create magnetic resonance without magnetic
materials [18, 20, 35], it in fact exhibits resonance both magnetically and electrically
depending on the orientation of the split ring inside an electromagnetic field [29, 35-39]. An
electromagnetic wave is propagating along the k direction in Figure 2.2. The electric field (E)
and the magnetic field (H) are perpendicular to each other, and the alternating magnetic field
passing through the ring generates current on the conductive trace. As a result, electric
charges are accumulated across the gap on the SRR, leading to electric energy being stored in
the gap and magnetic field energy inside the region enclosed by the ring. Therefore, the
resonance of the SRR can be characterised by the effective capacitance coming from the gap
and effective inductance coming from the conductive loop. Hence equation 2.1 is fulfilled.
This behaviour is unaffected for both orientations in Figure 2.2(a) and (b). However, the
electric field acting on the ring in Figure 2.2(a) is parallel to the gap, and due to the
asymmetric layout of the ring in the electric field, charges accumulated on the ring to move in
the same direction, so does the current.
16
(a) (b)
Figure 2.2: The split ring resonator in electromagnetic field with different orientations. (a) the
gap is parallel to the E-field, (b) the gap is perpendicular to the E-field.
The orientation in Figure 2.2(b) depicts the gap of the SRR perpendicular to the electric field.
The symmetric geometry of the SRR on each side of the gap generates charges moving in
opposite directions, which eliminates the generation of current and electric resonance is
suppressed. Though it is easier to understand the electric resonance and magnetic resonance
separately, they are usually hybridized resulting in the complicated bianisotropic
phenomenon [40-42]. In general, it is clear that the orientation of the SRR in an incident
field affects its performance.
2.2.3 Split Ring Resonator Coupling
Magnetic resonance is realised by an individual SRR responding to the varying magnetic
field, but this alone is not sufficient to show negative permittivity [11, 43-46]. The
periodicity of SRRs is essential to the composition of metamaterials. Further, its use in
metamaterials, investigations into the coupling between two closely-spaced SRRs provides a
17
significant boost to the performance of the SRR and unlocks auxiliary potential by the
addition of design parameters and degrees of freedom [36, 45, 47].
Coupled SRRs are often classified as edge coupled, and broad-side coupled depending on
their arrangement [48, 49]. The edge coupled SRRs illustrated in Figure 2.3(a) consist of two
concentric but different radius SRRs with splits facing opposite directions [23]. This
structure is also known as double split ring resonator (DSRR) [50]. As it was presented in [1]
as the first SRR, these edge coupled SRRs are typically seen as the original form of a SRR.
Edge coupled SRRs can also be two adjacent SRRs placed in the same plane as shown in
Figure 2.3(b). The effect of the physical arrangement of edge coupled SRRs has been
investigated in [44, 51-55]. It is shown that the rotational angle of an individual split ring in
the electromagnetic field has minor but noticeable effects on the transmission response.
However, the relative rotational angle between coupled SRRs has a larger impact on the
mutual inductance and capacitance of the overall structure, resulting significant frequency
shift. The relative angle of coupled SRRs also contributes to how much the lateral space
between them will affect the transmission response. A smaller relative rotational angle is
reported to cause larger frequency shift due to the increasing space between edge coupled
SRRs. Broad-side coupled SRRs were first introduced in [40] to avoid the bianisotropic effect.
They are defined by placing one ring directly opposite to another identical ring on other side
of the substrate, with the splits facing to opposite directions as shown in Figure 2.3(c). The
resulting opposite current direction through two rings eliminates the bianisotropic effect
caused by traditional edge coupled SRRs, which contains two concentric rings with current in
the same direction. Further investigations have been established into broad-side coupled
SRRs [56-62], with all demonstrated results showing that the resonant frequency of the
broad-side coupled SRR is related to both the relative orientation of each SRR and their
separation. This is similar to edge coupled SRRs with the addition of vertical separation
18
between them, perpendicular to the planes of SRRs. The vertical separation is reported to be
inversely proportional to both the mutual inductance and capacitance. Increasing the vertical
separation between broad-side coupled SRRs would induce an increase in resonant frequency,
until the space is too large for efficient coupling.
(a) (b)
(c) (d)
Figure 2.3: Different coupling modes of SRRs, (a) conventional edge coupled SRRs, (b)
modified edge coupled SRRs, (c) conventional broad-side coupled SRRs, (d) modified broad-
side coupled SRRs.
19
2.3 RF devices incorporating SRRs
The SRR has been widely used to make and improve a variety of RF devices due to its small
physical profile and high potential for reconfigurability. A review of some of the
applications of SRR in RF circuit design was presented in [16]. Filters or RF absorbers
implemented with SRRs have been shown to provide higher quality factor and low radiation
loss. The rejection band of the filter can be adjusted by the size of the implemented SRRs
[63, 64]. The variety shapes and numbers of SRRs used in the filter structure can also be an
effective method to create multi-band filtering effects [65-67].
As mentioned previously, the SRR can be considered as an L-C circuit, meaning any changes
to the effective inductance and capacitance value has an influence on the resonant frequency
of the structure. This characteristic is primarily used in the design of sensor systems.
Samples are either placed precisely on the gap or dropped directly on the surface of the SRR,
and the changes to the effective L-C values reflect on the shifted resonant frequency which
can be measured and evaluated [68-72].
The high quality factor, small electrical length and planar geometry of the SRR can be
utilised in the design of an antenna for optimal performance. Different shapes and numbers
of split rings can be used to enable multi-band antenna structures [73-76]. Also, the
orientation of a SRR placed next to antenna can adjust the operation frequency [77].
The benefit of implementing SRRs in a variety of passive RF devices has been demonstrated
in this section. The size, quantity, orientation, geometry and locations of the SRR can all be
determining factors to the performance of the devices. Investigations into the characteristic
behaviour and controllability of SRRs broaden its implications in RF devices, and introduce
new potential benefits to RF systems.
20
2.4 Reconfigurable resonator structures
The SRR has been proven to improve the function of passive RF devices dramatically for
some applications. However, the SRR is also known to suffer from a narrowband frequency
response. SRR based devices will not be operational unless the strict bandwidth conditions
have been met, and these conditions can vary with changes to the surrounding components or
system, and the environment in which it operates. To adjust the operation of the device after
fabrication, the SRR needs to be redesigned to compensate for the desired performance, and
the entire structure must be reproduced. To overcome this problem, a reconfigurable SRR
response will have more applicability and provide solutions for a greater range of scenarios,
such as reconfigurable filters [78] and antennas [79]. A comprehensive review of current
reconfiguration approaches is presented below.
2.5 Reconfiguration Mechanisms
2.5.1 External Components
The inclusion of external components such as capacitors, varactors, MEMS, and motors
provide common convenient methods to adjust both electrical and physical properties of a
SRR. They can be classified by their underlying mechanism as electrical, electrical-
mechanical and mechanical modifications. However, these examples are only a few of the
techniques available for tuning or reconfiguration of SRRs. A more comprehensive survey is
provided in this section.
21
Electrical modification:
Earlier attempts at pursuing reconfigurable SRRs utilise a capacitor to join the open ends of
the split ring. The capacitance of the split ring is no longer predefined by the size and
material of the gap. Instead, the capacitance is adjustable by the capacitor in the gap [80, 81]
as shown in Figure 2.4 (a). The resonant frequency is changed by varying the value of the
selected capacitor. This technique is further developed by replacing the fixed value capacitor
with varactor elements. Since the varactor diode directly links with two ends of the
conductive loop of the split ring (as depicted in Figure 2.4 (b)), the capacitance in the system
is determined by the current value of the diode, which can be changed by applying external
voltage [82-90]. The capacitance of the varactor is inversely proportional to the applied DC
voltage. Thus the resonant frequency is reduced with a higher value of external voltage. A
similar technique is shown in Figure 2.4 (c) [91-93], where the capacitive components are
sensitive to exposed light. The intensity of the light, which can be adjusted by tuning the
supplied voltage, changes the capacitance of the diode resulting in frequency shift. The rapid
progress in materials science also forecasts reconfigurable SRRs by introducing voltage-
active materials [94, 95]. However, the extra components added to the gap of the SRR (e.g.
varactors or advanced material), all requiring wiring to supply the DC voltage. This network
of wires or printed tracks brings interference to the system, especially to the electromagnetic
field, resulting in additional losses due to reflection and coupling with adjacent parts. It also
adds bulk to a planar SRR structure, which deviates from its raison d'etre.
22
(a) (b) (c)
Figure 2.4: Electrical components for reconfigurable SRRs (a) capacitor loaded [80], (b)
varactor-diode loaded [83], (c) photon-diode loaded [91].
Reconfiguration without the addition of components requiring connection to an external DC
source can be achieved with unique materials loaded into the SRR to purposely enable
property dependence from a wide range of external stimulation. For instance, SRRs created
with superconductor, semiconductor or ceramic composite elements can be dependent on the
thermal or DC magnetic environment [96-99], resulting in reconfiguration of their resonant
frequency. Although this form wireless stimulation does not increase the structural
complexity compared to a conventional SRR, the external magnetic field still causes
electromagnetic interference, and thermal effects can cause permanent changes to the
inherent SRR characteristics.
Electrical-mechanical modification:
Mechanical reconfiguration can be described as the structural modification of SRRs. The
driven force can come from both electrical and mechanical sources. The micro electro-
mechanical system as known as MEMS is overwhelming used to alter the internal structure of
RF devices. Its impact on the structural tuning of SRRs has increased in recent years. The
23
majority of the MEMS devices are based on electrostatic force, which is induced by a DC
bias [78, 100-103]. A MEMS switch is realised by placing a segment of metallic components
on an elastic cantilever. The electrostatic force induced by DC bias generates attraction or
repulsion force resulting in deformation of the structure. During this process, a SRR can be
actuated by short circuiting the metallic ring (Figure 2.5).
(a) (b)
(c)
Figure 2.5: A reconfigurable SRR using MEMs switch (a) off and (b) on stage of MEMS
switch [104], (c) photograph of MEMS switch [101]
Moreover, the orientation and separation of coupled SRRs can also be adjusted due to the
structural deformation. The performance of the MEMS strictly relies on the fabrication
24
technique, which significantly restricts its scalability and accuracy. Also, unless the MEMS
is created with magnetic materials that are responsive to the magnetic field [105] a DC bias is
still required to generate the mechanical force. Overall, MEMS switches provide effective
reconfigurability for SRRs, but suffer the same drawbacks of extensive bias networks and
interference as electrical component reconfiguration.
Mechanical modification:
Mechanical force can easily be manipulated by external devices. Small motors have been
employed to control the orientation of a SRR in an incident field to modify the resonant
frequency [106-108] as shown in Figure 2.6 (a). The resonant frequency shift phenomenon
can be attributed to the design of the mechanical rotation sensor [109]. Other degrees of
movement enabled by mechanical means include the introduction of the concept of lattice
shift [110-113], which is an effective approach to reconfiguring the resonant frequency of
metamaterials.
(a) (b)
Figure 2.6: Mechanical means of structure reconfiguration (a) motor driven rotation of SRR
[106], (b) stretchable SRR substrate [114].
25
Recently, progress on flexible materials and liquid metal structures have provided a new
dimension to the mechanical modification of SRRs. These SRRs are usually made with
flexible substrate [115-118] and infiltrated with liquid metal [114, 119] to allow bending,
stretching and compressing as demonstrated in Figure 2.6 (b). The results show that
reconfiguration of the resonant frequency under these mechanical processes.
Mechanical forces coming from either the core mechanical devices, such as motors, conveyor
or human hands are believed to enable reconfiguration of SRRs. However, the requirement
condition of operation RF devices under electromagnetic excitation is crucial. The
interference caused by the external source of the mechanical force cannot be neglected. The
alteration of the structure relies on the accuracy of the mechanical devices and repeatability
of the structure, which can limit their feasibility in many RF environments.
2.5.2 Microfluidic/Pneumatic modification
A recent method introduces tunable SRRs using microfluidic reconfiguration [120, 121]. The
liquid metal is pumped into a pre-made fluid channel. Depending on the volume of the liquid
and the pump pressure, the liquid metal can be positioned at a specific location of the metallic
pattern. This determines the orientation of the open split of the SRR. A similar approach is
used to design a filter with SRRs [122]. The amount of pressure determines the length of the
liquid metal occupying inside the microfluidic channel that is intentionally made with the
shape of a SRR. Alternatively, a layer of liquid can be placed directly on top of the SRR
[123], and the different compositions of the liquid are shown to change the transmission
noticeably. The problem with using microfluidic reconfiguration comes from the
26
inconsistency of the pump pressure causing variation in the volume of the fluid. The residue
of the liquid inside the channel may also bring uncertainty to the system operation.
Figure 2.7: Reconfigurable SRRs using Microfluidic channels [120].
Pneumatic actuation has been used for pumping fluids through microchannels [124, 125].
Pneumatic switches have also been introduced to reconfigure resonators. By relocating a
partial metallic pattern from the original structure to an elastic membrane, a valve can be
formed between them as shown in Figure 2.8(a). Pneumatic pressure can change the relative
location of the electric components by providing positive or negative pressure inside the
valve [126-129]. Also, the pneumatic pressure can be used as a contactless mechanical force
in MEMS system [130], so the split ring can be bent around an elastic supporting bridge as
shown in Figure 2.8(b).
27
(a)
(b)
Figure 2.8: Reconfigurable SRRs using pneumatic actuation (a) pneumatic switch in off and
on stage [126], (b) behaviour of tunable SRR using pneumatic force [130]
The introduction of pneumatic actuation does not bring the undesired electromagnetic
interference of electrical biased and mechanical structures. However, the current pneumatic
switches suffer from complicated fabrication techniques and the manual alignment of
different layers which leads to inaccuracy.
28
2.6 Summary
A reconfigurable SRR substantially increases its application in passive RF devices, unlocking
its potential in the wider range of systems due to more flexible operational conditions. As
discussed in this chapter, there is a larger amount of literature to enable reconfiguration of
SRR based on DC biased active components, and mechanical switches. The latest
approaches featuring microfluidic and pneumatic actuation have also been discussed. The
common problems of the reconfigurable systems are the electromagnetic interference is
caused by additional electric components and their bias networks, the inaccuracy in the layout
of the structure due to complicated fabrication, and consistency of operation after repetitive
deformation. A comprehensive analysis of each method covering their key components and
limitations is summarized in Table 2.1.
Pneumatic force provides the benefit of not introducing extra electric components, and the
electromagnetic interference can be minimised as reconfiguration can be achieved purely by
maneuvering the near-perfect dielectric material, air. As stated in Section 1.3, the primary
aim of this research is to apply pneumatic levitation concepts to realise reconfiguration of
coupled SRR architectures. A variety of structures is investigated to modify the effective
capacitance within the SRRs systems via controllable and consistent means.
29
Table 2.1: Summary of conventional frequency reconfiguration technique
Frequency
Reconfiguratio
n Techniques
External Components Microfluidic/Pneumatic Modification
Electrical
Modification
Electrical-Mechanical
Modification
Mechanical
Modification
Microfluidic Pneumatic
Key
Components
• Extra diode and
capacitor
• Thermal/magnetic
reactive materials
• MEMS
• Motor
• External force
• Liquid metal
• Pneumatic switch
Limitations • Extra components
wired to the DC
voltage cause
electromagnetic
interference
• External magnetic
field disturbs the
original field
• Thermal effect may
result permanent
changes
• The performance of
the MEMS depends
on the fabrication
technique, resulting
limited scalability and
accuracy.
• DC bias required to
generate the
mechanical force
causes interference
• Mechanical force
requires external
device that brings
interference.
• The dependence of
the mechanical
source limits the RF
environments
• Inconsistency of the
pump pressure
causes variation in
the volume of the
fluid.
• Residue of the liquid
inside the channel
brings uncertainty to
the system operation
• Complicated
fabrication and
manual alignment
leads to inaccuracy
30
CHAPTER 3
Dynamic resonator tuning by pneumatic levitation
3.1 Introduction
The implementation of SRRs as a key electromagnetic component in microwave devices,
transmission line structures, metamaterials and metasurfaces has seen rapid expansion over
the past few years. The properties of the SRR have also been extensively analyzed. The SRR
consists of a conductive wire loop with a small gap between each end. However, due to the
naturally narrow bandwidth of SRR, the capacity to adjust the frequency of SRR becomes
vastly important. The position of the gap, and hence the mutual orientation of the SRR in the
incident electromagnetic field causes variance in its resonant frequency. This property can be
utilised to design tunable RF components such as a frequency configurable antenna [77].
However, in this technique, the tunability of the RF component is limited by the static
orientation of the printed split rings. Dynamically changing the orientation of the SRR will
provide a swept resonant frequency akin to scanning systems such as radar and sensors.
Coupled SRRs usually consist of a group of more than one identical SRRs. The
electromagnetic properties of a coupled SRRs system are determined by design of the
individual split ring and their mutual interaction. The relative orientation of the SRRs, which
is determined by the direction of their split in an electromagnetic field, is an important factor
in their mutual relation.
Following the methodology shown in Figure 3.1, this chapter will investigate and
demonstrate a pneumatic levitation concept to perform structural tuning of the response of
SRRs. A contactless platform controlled by pneumatic force is proposed to dynamically
31
change the orientation of SRRs represented relative to an incident electromagnetic wave in
azimuthal plane. This approach is designed to encounter less electromagnetic interference
than traditional tuning methods as the SRR is manipulated solely by air and no metallic
bias/control line are required. The levitation platform also restricts the movement of the SRR
to one degree of freedom only. Therefore, the resonant frequency is adjusted by controlling
an individual structural parameter.
Figure 3.1: Flowchart showing the methodology for this research. Sections in orange are not
discussed in this chapter.
32
3.2 Design of the split ring resonator
Edge coupling is the classic coupling mode of a pair of SRRs. As the name indicates, split
rings are neighboured or concentric in the same horizontal plane. In contrast, broad-side
coupled SRRs are constructed with metallization parallel to the plane of the structure on
opposite sides of a dielectric substrate. They were introduced in 2002 with the purpose of
removing undesired bianisotropic phenomena found in edge-coupled SRRs in early research,
as well as being easier to fabricate. This chapter is devoted to exploring the mutual coupling
of a pair of broad-side coupled SRRs with the relative orientation manipulated by pneumatic
levitation. The SRRs equivalent L-C circuit is shown in Figure 3.2 (b). Theoretically, the
conductive trace is characterised as an inductance. The mutual inductance between two rings
is minor compared to the self-inductance according to loop antenna theory. The inductance of
the whole system is represented by L. Cs is the capacitance due to the splits on the rings, Co is
used to describe the mutual capacitance between two rings which in this chapter establishes
the possibility of frequency tunability. Changes to the mutual capacitance will result in
different transmission properties for a pair of broad-side coupled SRRs.
Structural tuning is achieved by defining the rotation angle (indicated in Figure 3.2 (a)) as the
governing parameter to alter the mutual capacitance between a pair of broadside coupled
SRRs. The increasing rotation angle enlarges the mutual capacitance of the system. The
resonant frequency is expected to drop up to 180o. Hence it returns back to normal from 180 o
to 360 o.
33
(a)
(b)
Figure 3.2: (a) Broad-side coupled SRRs structure and (b) the equivalent circuit
The coupled SRRs used in this chapter are different from traditional broad-side coupled split
rings, which share the substrate. Two identical split rings residing on their own substrates
with the conductive loops facing inwards are separated by a layer of air. Thus, the thickness
of the layer of air determines the separation of the two broad-side coupled SRRs.
34
3.3 Pneumatic levitation structure
3.3.1 Design Concept
Figure 3.3 depicts the schematic of the platform used to control the SRRs. Air is pushed
through multiple orifices in a base platform which applied a balanced lifting momentum to
the levitation platform positioned above. The ridge around the bottom of the platform
inspired by the skirt on hovercraft is designed to trap the air and form pressure differential
between the space above and under the levitation platform. This lowers requirements on the
levitation force and encounters lower turbulence. The lower SRR (Ring 1) is static on the
base platform, while the upper SRR (Ring 2) is secured on the levitation platform. Since
Ring 2 is placed on the levitation platform, its movement is synchronized with the levitation
platform.
Figure 3.3: Schematic of the levitation concept
Apart from the core benefits of using the pneumatic system which eliminate most the
electromagnetic interference caused by extra metallic structures, another advantage is it
35
establishes contactless control of SRRs, and has the potential to restrict movement to only
one degree of freedom. The levitation structure can be designed to only enable rotation in the
azimuthal plane around the axis passing origins of both SRRs. However, the pneumatic force
around the outer geometry of the levitation platform must be maintained to counterbalance
the gravity of the structure.
3.3.2 Fluid simulation
The core concept illustrated in Figure 3.3 is analyzed using ANSYS fluid simulation. A
variety of parameters is taken into account with the purpose of designing an operational and
stable pneumatic levitation system.
Dimensions of the pneumatic structure: The pneumatic levitation system aims to aid in the
structural tuning of broadside-coupled SRRs. Evaluating the electromagnetic response of the
tunable SRRs is essential. A rectangular waveguide will be used to quantify the SRR
response. Hence the dimensions of the waveguide aperture determine the upper limit of the
size for the entire levitation system.
The size of levitation platform: The levitation platform must be large enough to fit a SRR at
the desired frequency. Additionally, to remove the impact of the physical properties of the
SRRs, the platform is designed to be significantly larger and heavier than the SRR for high
stiffness and air damping. In order to avoid the unnecessary degree of freedom in the
movement of a levitation platform floating freely platform on an air surface, the platform is
placed inside a small chamber just larger than the platform itself, to enable lateral
36
confinement. The periphery of the platform together with the confinement chamber also
determines the paths for air to flow, therefore significantly influencing the aerodynamics.
The design of the air floor: The air floor restricts the air flow coming from the external source
and distributes the air evenly across the under-side of the levitation platform. The thickness,
shape, and layout of the air floor layer and air orifices are analyzed in simulation to provide
high stiffness.
The fluid simulation is used to visualise the dynamic pressure, turbulence, and velocity of the
air flow inside the levitation system. All parameters are optimized based on both inspection
of fluid simulation results and verification of prototype measurement. Figure 3.4 shows the
cross-section of the proposed structure. The air is pumped from the air inlet and stored in the
air chamber before being delivered to lift the levitation platform. The airflow goes through
the channel formed by the peripheral of the levitation platform and the confinement wall.
Figure 3.4: Cross-section of the pneumatic levitation structure for fluid simulation.
37
Figure 3.5 display the fluid analysis results for determining the dimensions of the levitation
platform. Figures 3.5(a), (c) and (e) indicate the simulation result of an undersized platform.
Figures 3.5(b), (d) and (f) on the other hand show the oversized platform. Comparing the
dynamic pressure results in Figures 3.5(a) and (b), there is a significantly higher level of
pressure in Figures 3.5(b) around the side of the platform due to higher restricted air in a
narrower space. The velocity shown in (d) reflects a higher air flow speed, explained by the
Bernoulli’s effect.[131, 132]. The turbulence level in Figures 3.5(f) is also too high on all
sides of the oversized levitation platform. For the undersized platform, due to the extra space
between the levitation platform and confinement wall, the air creates a vortex inside the space
which causes turbulence. Also, the pressure around the side of the platform would not be
sufficient to limit it to a central location, allowing lateral drift. The other parameters of the
levitation structure were all studies via a similar process to optimise the structural dimensions.
38
(a) (b)
(c) (d)
(e) (f)
Figure 3.5: Fluid simulations showing the cross-section of the levitation structure
(a) small dynamic pressure due to the large channel, (b) excessive dynamic pressure due to
tide channel, (c) low air flow velocity, (d) high air flow velocity, (e) turbulence level with the
large channel, (f) the turbulence level with small channel.
3.3.3 Assembly of the pneumatic levitation system
Figure. 3.6 (a) shows the cross-section of the final pneumatic levitation platform. Air is
delivered from a tube at the base of the structure and is temporarily stored in the conical air
chamber. The retarded air is well distributed in the cone-shaped chamber, and air flows
39
through eighteen evenly spaced 0.65 mm diameter air orifices on the air floor layer of the
structure in a circular geometry. This enables the levitation platform to be lifted by uniform
air pressure across its bottom surface. The conclusion is drawn based on the analysis of
different air floor prototypes. The greater the quantity of orifices with a smaller diameter is
proved to provide the most stable levitation force. The length a of the upper module is 34
mm, designed to fit into a WR-284 waveguide. The height b of the top module is 15 mm
which provide enough confinement for the levitation platform. In addition, the assembled
height including the lower module height c = 25 mm, locates the corresponding
electromagnetic components in the centre of the measuring waveguide. The thickness e of
the upper module is 1 mm, leaving enough clearance for the design of the levitation platform
without sacrificing the structural firmness.
(a) (b)
Figure. 3.6: (a) Layout of the levitation structure (b) the levitation platform
Figure. 3.6 (b) depicts the underside of a standard levitation platform design. The skirt aims
to trap air and create an air pressure difference above and below the platform. The air
40
escaping from underneath the levitation platform flows through the small gap between the
side of the platform and wall of the outside confinement structure in Figure. 3.6 (a). This
creates a laminar flow, securing the platform axially in the centre. The diameter of the
levitation platform is 30 mm. Hence, the space between the levitation platform and the outer
confinement is 1 mm, which is proved both theoretically and experimentally to provide
enough air flow to centralise the platform without introducing excessive turbulence to the
levitation system. The thickness T of the outer boundary of the levitation platform is 2.5 mm.
The thickness determines whether the air tunnel formed by the confinement wall and side of
the platform allows the air to evacuate with a minimum of turbulence and uniform pressure.
The amount of the skirt height h and width s are both 0.5 mm to again minimise turbulence
with noticeably less pneumatic pressure for stable levitation.
3.3.4 Prototype fabrication
All pneumatic structures were fabricated using a micro-miller (isel-CNC CPM 4030-Isel).
Each component is drawn on a 2D graph with an assigned depth in Galaad v3, and associated
with different sizes of milling cutters. Large diameter cutters are used when bulk material is
being removed, or a smooth surface is required. Smaller diameter cutters are used to increase
precision and specific dimension requirements such as the diameter of the air orifices.
Polymethyl methacrylate (PMMA) is used as the main building material for the levitation
structure due to its optical transparency (to observe operation) and easy machinability.
3.3.5 Experimental confirmation of the levitation
The free rotation of a SRR in the azimuthal plane is enabled with a minimum of friction when
the levitation platform loses contact with the underneath surface fully. To test whether the
41
structure depicted in Figure 3.6 successfully provides levitation, an experiment is conducted
to examine the potential of the levitation system.
The levitation structure shown in Figure 3.6 is tested using the equipment setup in Figure 3.7.
An air pump is used to create the initial air pressure, which is connected to a tank large
enough to convert the pulsed air generated by pistol based pump to smooth, linear air
pressure. A valve attached on top of the tank controls the pressure level contained in the
reservoir. A pressure meter detects the static pressure parallel to the outlet of the tank as the
air is delivered via a tube to a small hole in a WR-284 rectangular waveguide located directly
below the levitation structure. Exhaust holes are placed above the levitation module to help
to regulate the pressure inside the waveguide. By controlling both the air pump and valve on
the tank, levitation of the platform can be achieved. A DSLR camera mounted directly in
front of the waveguide captures the cross section of the levitation structure. Thanks to the
transparency of the PMMA, sharp focus and minimal image noise is achieved. The shape of
the platform can be captured when the light source is coming straight to the camera lens
through the levitation structure.
(a)
42
(b)
Figure 3.7: (a) Schematic of the experimental setup for levitation; (b) photograph of the
experimental setup.
Figure 3.8 demonstrates the levitation platform under different amount of pressure. Figure
3.8(b) is noticeably higher than Figure 3.8(a) due to higher pneumatic pressure resulting in a
larger levitation distance. The images were analyzed using computer software to measure
distance based on pixel count. Comparing to a reference length on the image, the
approximate levitation height can be evaluated corresponding to different pneumatic
pressures.
43
(a) ( b)
Figure 3.8: The photographs taken for the cross-section of the levitation structure (a) no
pneumatic pressure, (b) high pneumatic pressure.
Figure 3.9: Levitation heights with different amount of pneumatic pressure.
0 100 200 300 400 500
0.00
0.05
0.10
0.15
0.20
Lev
itat
ion
(m
m)
Pneumatic Pressure (Pa)
44
The results in Figure 3.9 display the levitation potential of the new platform. With a growing
level of pressure, the platform can be levitated gradually up to 0.2 mm. Further increased
pressure would lose the stability of the levitation. The results successfully prove the
levitation platform is completely losing contact with the air floor. Therefore minimal friction
is acting on the platform.
3.4. Dynamic tuning of split ring resonator
3.4.1 Design of levitation platform
The fundamental structure described in Section 3.3.3 and experimentally verified in Section
3.3.5 has the advantage that each component is individually designed and fabricated then
assembled. This allows the levitation platform to be tailored or exchanged to fit into different
applications with dedicated engineering design.
(a) (b)
45
(c)
Figure 3.10: 3D rendering of the underside of various levitation platforms
Figure 3.10 depicts three different levitation platform designs used to provide continuous
spinning motion. Further to the basic platform design shown in Figure 3.6 (b), rotational
momentum is created in Figure 3.10(a) by adding an even number of angular slots
symmetrically cut into the skirt to provide paths for air flow and spin the platform on its axis.
The slots are cut at 45 degrees to the tangent of the circle. Figure 3.10(a) features four slots
cut in the skirt, Figure 3.10(b) has eight slots, and Figure 3.10(c) has four with centrifugal
groove patterns connected inwards to the slots. The self-spinning also increases the stability
of the platform due to gyroscope stability. In addition, the spinning motion due to the cut
slots prevents the platform from levitating higher than necessary. The SRR is secured onto
the top surface of the levitation platform, hence the orientation of the split will be
synchronized with the platform.
3.4.2 Simulation
46
Two identical SRRs are designed and fabricated to test whether dynamic tunability of the
coupled SRRs can be achieved with the pneumatic levitation structure.
Figure 3.11: Schematic of the broad-side coupled SRRs.
As shown in Figure 3.11, the orientation of the incident electromagnetic wave is parallel to
the plane of the SRRs. The electric field is in the same plane as the SRRs as well, with the
magnetic field perpendicular. The outer radius r of the conductive loop is 6 mm, the width of
the conductive trace w and the size of the split g are 0.5 mm. The orientation angles θ and β
represent the direction of the top and bottom SRR respectively. R and t represent the radius
and thickness of the substrate with values of 7 mm and 0.508 mm respectively. Finally, s is
the separation of two rings, equal to 2 mm.
Initially, ANSYS HFSS is used to predict the resonant response of a single SRR as a result of
the pneumatically induced spinning motion. The dynamic variation is represented by a
combination of static SRR simulations at various rotation angles θ. The rotation angle θ is
increased from initial 0° to 180° in 15° increments. Due to the symmetric structure of the
SRR, its behavior from 180° to 360° can be well described by reversing the results in the 0°
to 180° range. As shown in Figure 3.12(a) and (b) the resonant frequency decreases from
47
3.041 GHz to 3.03 GHz with increasing rotation angle θ from 0° to 90°. The resonant
frequency increases and returns to its original frequency with increasing angle from 90° to
180°. The electromagnetic results demonstrate a full cycle of resonant frequency shift as the
split ring is spinning inside the waveguide, as the sweep repeats from 180° to 360°.
(a) (b)
Figure 3.12: Simulation results of |S21| with different rotational angle θ in a single SRR
The simulation indicates the dynamic change in orientation of the split ring due to the
constant spinning motion cause the resonant frequency to sweep. The amount of shift is
limited by the relative subtle changes to inherent inductance and capacitance of a single SRR
about the orientation of the incident electromagnetic wave. Thus, the electromagnetic
properties of single SRR are less impacted by the orientation changes.
In order to increase the range of frequency sweep, another identical SRR is secured into the
air floor directly under the levitation platform where the dynamic split ring is attached. This
creates the broad-side coupled SRR system described in Figure 3.11. While the bottom ring
remains static at 0 degrees to the electromagnetic propagation direction, the orientation
change of the top split ring will cause the mutual coupling between two rings to alter as the
result of the spinning platform. Figure 3.13 illustrates the simulated results showing the
resonant frequency shift due to the dynamic changes in the relative orientations of the SRRs.
2.96 2.98 3.00 3.02 3.04 3.06-25
-20
-15
-10
-5
0
Frequency (GHz)
|S21| (
dB
)
0o
15o
30o
45o
60o
75o
90o
2.96 2.98 3.00 3.02 3.04 3.06-25
-20
-15
-10
-5
0
|S21| (
dB
)
Frequency (GHz)
90o
105o
120o
135o
150o
165o
180o
48
Theoretically, the resonance of the coupled split ring can be shifted between 2.7 GHz to 2.36
GHz as the top ring rotating from 0o to 180o. Moreover, the results reverse from 180o to 360o
due to the symmetric structure.
Figure 3.13: Simulation results of |S21| with bottom SRR at 0 degrees and 2 mm from the top
SRR
Figure 3.14: Simulation results of |S21| with bottom SRR at 90 degrees and 2 mm from the top
SRR
The orientation of the lower SRR also affects the transmission results of the coupled SRRs
due to the relative orientation in the incident field. Figure 3.14 shows the simulation results
2.3 2.4 2.5 2.6 2.7 2.8-30
-25
-20
-15
-10
-5
0
0o 15
o
30o 45
o
60o
75o
90o
105o
120o
135o
150o
165o
180o
Frequency (GHz)
|S21| (
dB
)
2.3 2.4 2.5 2.6 2.7 2.8-30
-25
-20
-15
-10
-5
0
|S21| (
dB
)
Frequency (GHz)
90o 105
o
120o 135
o
150o
165o
180o
195o
210o
225o
240o
255o
270o
49
with top ring rotating around its axis while the lower ring is placed at 90 degrees to the wave
propagation direction. This converts the symmetric of the structure from 0o-180o to 90o-270o.
The transmission results show that the resonant frequency decreases as the top ring rotates
clockwise, similar to the results in Figure 3.13. However, the magnitude of S21 and narrower
range of the shift indicates the coupled resonance between two SRRs is lowered. This is
related to the bottom ring remaining static with the split perpendicular to the electric field.
Due to the symmetry of the split to the electric field, the current induced on the both sides of
the split on the bottom ring are in different directions, and therefore are partially cancelled.
3.4.3 Experimental setup and mechanical measurement
Fig. 3.14 shows the experimental set-up used to quantify the dynamic transmission response
of the pneumatically levitated SRR with different applied air pressures. Similar to the setup
in Section 3.3.5, the regulated air is injected into the levitation structure inside the waveguide,
which has both ports connected to an Agilent E5071B vector network analyzer. By
controlling both the air pump and valve on the tank, levitation of the platform can be
activated to allow free spinning of the levitation platform. The spinning speed can be
controlled by the air pressure, and the vector network analyzer records the dynamic
transmission response.
50
Figure 3.15: Experimental setup
3.4.4 Measurement
The transmission measurements in Figure 3.16 (and summarised in Table 3.1) are taken with
the top SRR statically placed at the corresponding rotation angles inside the WR284
waveguide. A resonant frequency shift is observed with increasing of rotation angle θ. A full
cycle of resonant frequency decreasing and increasing provides the experimental evidence of
the operation of the system to validate the simulations.
51
(a) (b)
Figure 3.16: Measurement results for rotation of the top statically placed SRR
Table 3.1: Summary of the simulated and measured resonant frequencies
θ Simulation Measurement
0 3.04 3
30 3.036 2.998
60 3.033 2.987
90 3.03 2.981
120 3.034 2.984
150 3.036 2.993
180 3.04 2.998
The broad-side coupled SRRs are also measured with the top ring sitting at each comparable
rotation angle while keeping the bottom SRR stationary on the air floor. The frequency
sweep is also observed with pneumatic pressure applied. Figure 3.17 and Figure 3.18 display
the transmission measurement of the broad-side coupled SRRs, and the results are
summarised in Table 3.2 and 3.3.
2.96 2.98 3.00 3.02 3.04 3.06-25
-20
-15
-10
-5
0|S
21| (
dB
)
Frequency (GHz)
0o
15o
30o
45o
60o
75o
90o
2.96 2.98 3.00 3.02 3.04 3.06-25
-20
-15
-10
-5
0
|S21| (
dB
)
Frequency (GHz)
90o
105o
120o
135o
150o
165o
180o
52
Fig. 3.17: |S21| for rotation angle θ statically from 0° to 180° and lower SRR at 0o
Fig. 3.18: |S21| for rotation angle θ statically from 0° to 180° and lower SRR at 90o
Table 3.2: Resonant frequencies for broad-side coupled SRRs with lower SRR at 0 degrees.
Simulation Measurement
0 2.7 GHz 2.67
30 2.66 GHz 2.62
60 2.59 GHz 2.53
90 2.48 GHz 2.48
120 2.42 GHz 2.43
150 2.37 GHz 2.4
180 2.36 GHz 2.38
Range 13% 11%
2.3 2.4 2.5 2.6 2.7 2.8-30
-25
-20
-15
-10
-5
0|S
21| (
dB
)
Frequency (GHz)
0o 15
o 30
o 45
o 60
o 75
o 90
o
105o
120o
135o
150o
165o
180o
2.3 2.4 2.5 2.6 2.7 2.8-30
-25
-20
-15
-10
-5
0
|S21| (
dB
)
Frequency (GHz)
90o 105
o 120
o 135
o 150
o 165
o 180
o
195o
210o
225o
240o
255o
270o
53
Table 3.3: Resonant frequencies for broad-side coupled SRRs with lower SRR at 90 degrees.
Simulation Measurement
90 2.65 2.66
120 2.63 2.6
150 2.57 2.54
180 2.48 2.48
210 2.41 2.43
240 2.37 2.4
270 2.33 2.39
Range 12% 10%
The congruence of the simulation and measurement prove the successful implementation of
the pneumatic levitation structure to dynamically tune the coupled SRRs.
The resonant response is also recorded when pneumatic force is applied. Dynamic results
taken from the recording of the continuously sweeping transmission match the static
measurements in Figure 3.16 and provide the necessary information to analyze the spinning
speed of the platform.
Figure 3.19: Spinning speed profile respond to pneumatic pressure
200 400 600 800 1000
0.0
0.5
1.0
1.5
2.0
8 Slots
4 Slots
4 Slots with grooves
Ro
tati
on
Fre
qu
en
cy
(H
z)
Pressure (Pa)
54
The spinning speed of the different levitation platforms shown in Figure 3.10 was determined
through analyzing the experimental transmission results. According to the Bernoulli’s
principle:
v2
2+ gz +
p
ρ= constant (1)
where v = fluid flow speed at the chosen point, g = acceleration of gravity, z = elevation of
the point, p = static pressure at the point, and ρ = density of the fluid.
The total pressure applied to the levitation platform is the sum of the static and dynamic
pressure. By injecting more air from the tank, the total pressure applied to the levitation
platform increases. The static pressure is constant at its maximum, which counter-balances
the weight of the platform. The extra pressure converts to rotational momentum as it
exhausts through the open angular slots around the skirt. The more pressure that is applied to
the system, the more angular momentum it produces; therefore, the faster the platform rotates.
When the discharge of air through slots reaches its maximum, a level which is dependent on
physical construction factors, additional pressure will elevate the platform higher and create a
“curtain area” for trapped air to escape until the balance is restored between the gravitational
and lifting forces in the system. This phenomenon is represented as a deceleration with
increasing applied pressure in Figure 3.19. All three levitation platforms rotate faster as the
pressure increases and decelerate when the pressure is further increased. The results also
confirm the values collected in Section 3.3.5. The platform can absorb a certain level of
force before losing its stability, which may impact the spinning motion due to excessive
pneumatic force converted to levitation. Additionally, the structures appeared to require a
different minimum pressure in order to commence rotation and have a distinct sensitivity to
the applied pressure. The platform with eight slots requires more initial pressure to start
rotation but accelerates its maximum speed quickly. The four slot platform rotates at very
55
low pressures but gradually increases to its maximum speed. The platform with four open
slots connected to clockwise spiral groove from the centre to guide the air on the underside
requires an intermediate amount of pressure to start rotating but shows a dramatic escalation
of speed with increased pressure.
3.5 Summary
This chapter has demonstrated a novel pneumatic levitation system as a means of
dynamically controlling the relative rotation of broadside coupled SRRs. A frequency sweep
due to the comparative orientation change of the SRRs is demonstrated, with control over the
spinning speed using pneumatic force and platform design. This contactless air controlled
system can minimise the electromagnetic interference introduced by traditional frequency
tuning methods requiring metallic structures or bias lines in frequency scanning systems such
as radar and sensing applications.
56
CHAPTER 4
Pneumatic levitation reconfigurable coupled split ring resonators
4.1 Introduction
Recent studies have demonstrated different methods to achieve frequency reconfigurability in
SRR based systems. They can be broadly classified as electric tuning and mechanical tuning.
The traditional methods rely on high precision fabrication techniques such as lithography and
microfabrication, which imposes accuracy tolerance. The incorrect placement of the
switching element may also result in significantly deviated results. Also, the electromagnetic
field is sensitive to any conductive elements, which is unavoidable for electric components
and mechanical force generators.
Figure 4.1: Flowchart showing the methodology of this investigation. Sections in orange are
not discussed in this chapter.
57
In the previous chapter, a pneumatic levitation system is proposed successfully to provide
contactless and metal free platform for dynamically altering the orientation of a split ring in
an incident electromagnetic wave. Following the methodology shown in Figure 4.1, this
chapter introduced an advanced pneumatic levitation system with the capability to precisely
control the orientation direction of SRRs to the desired rotational angle for on-demand
reconfigurability without a sophisticated electrical or mechanical structure. In addition to the
rotational angle, the distance between two SRRs can also be reliably controlled by adjusting
the pneumatic pressure. The combination of both of these controls enables a large frequency
configuration range for broad-side coupled SRRs.
4.2 Pneumatic system design
4.2.1 Design Concept
Chapter 3 has shown that pneumatic levitation techniques can achieve dynamic SRR
frequency tunability. Although the resulting frequency sweep could benefit sensor and radar
systems, other RF applications undoubtedly favor a static operational frequency. The
reconfigurability of the SRRs is necessary to define a specific resonant frequency. The
challenge faced is to improve the pneumatic structure to provide discrete control over the
orientation of the SRRs.
4.2.2 Assembly of the structure
A cross-section of pneumatically controlled levitation system is shown in Figure 4.2. In a
similar way to the structure presented in Chapter 3, air flows from the bottom inlet and is
58
temporarily stored inside the air chamber. The cone shaped air chamber is designed to
provide enough room for air to distribute over a wider surface. The air flows through nineteen
orifices with 0.65 mm diameter on the air floor layer. The layout of the orifices is circularly
symmetric on the air floor to ensure the air coming through these orifices transforms to a
consistent lifting pressure. The same fluid simulation is undertaken to optimise every
dimension of the structure. Samples are engineered to provide experimental verification using
a versatile structure with stable levitation and smooth operation. Owing to the modular
design of the structure, each component can be independently analyzed and fabricated.
Figure 4.2: Cross-section of the levitation module. a = 34 mm, b = 15 mm, c = 1 mm, e = 25
mm
59
4.2.3 Principle of system operation
Figure 4.3 depicts a zoomed rendering of the air floor and levitation platform. The top section
is the levitation platform and the bottom component details the air floor layer with side
bumper. Different to the previous structure, the air floor comes together as a pair with the
levitation platform, and also assembles into the outer confinement structure. A skirt is also
used to trap air under the levitation platform and reduce the air flow speed around it. As a
result, a difference in pressure level between under and above the platform is created,
elevating the platform based on Bernoulli's theory (1). Four tilted slots are cut through the
levitation platform skirt with an angle of 45O. This allows a small portion of the air to escape
through these slots and creates a rotational momentum induced by the dynamic air flow.
Consequently, the levitated platform will spin around its centre axis if suitable pneumatic
pressure is applied. The circular bumper around the perimeter of the detached air floor layer
has two key functions. The first is to regulate the gap between the side of the levitation
platform and side confinement walls. Air escaping over the skirt and through the tilted slots
will create a less turbulent flow vertically along the side walls, ensuring the platform remains
centred and free to spin. Secondly, the novel bumper mechanism facilitates the control of the
levitation platform, enabling the spinning platform to be stopped at a designated position.
60
(a)
(b)
Figure 4.3: (a) 3D rendering of the levitation platform and air floor: r1 = 31 mm, H1 = 1.7 mm,
h1 = 0.5 mm, t1 = 0.5 mm, r2 = 29 mm, H2 = 2.5 mm, h2 = 0.5 mm, h3 = 1 mm, t2 = 0.5 mm,
(b) operation of the levitation and spin mechanism
Four symmetrically located teeth are placed on the side of the levitation platform, directly on
top of the tilted slots. Correspondingly, eight ridges are formed on the bumper of the air floor
layer. The operational mechanism of the controlled pneumatic levitation system is shown in
Figure 4.3(b). The teeth on levitation platform are initially stopped by the ridge on air floor.
As the levitation force increases, the platform is lifted. As soon as the teeth exceed the height
of the ridges, the platform spins clockwise as described above. Conversely, reducing the
levitation force will cause the platform to drop in altitude, and the next ridge will lock its
61
position. Only one tooth would be required to stop at each ridge. However, the coincident
four teeth and four cut slots on the levitation platform are artificially created to maintain the
gravity balance of the platform.
In order to ensure minimal inference on the aerodynamics of the structure, an embedded
recess is formed on both the underside of the levitation platform and the top surface of the air
floor to implant the SRRs. The relative angular orientation of the electromagnetically coupled
SRRs is hence synchronized to the rotation of the levitation platform.
4.2.4 Fabrication of the structure
The same fabrication procedure is undertaken to create the structure as used in Chapter 3. All
structures except the lower air chamber are fabricated independently in micro-miller (isel-
CNC CPM 4030-Isel) with PMMA as the material for its transparency and easy
machinability. The air chamber is replaced with 3D printed module made from Acrylonitrile
Butadiene Styrene (ABS) to form the smooth curvature of the cone shape.
4.3 Parameter range validation
The levitation potential of the new pneumatic system, which is the practical maximum
separation between coupled SRRs, needs to be examined. With revamped air floor and
levitation platform, the aerodynamic response is expected to be different. The outcome
provides the specified parameter range for both electromagnetic simulation and prototype
fabrication.
62
A setup identical to the one described in Section 3.3.5 is used to measure the levitation height
corresponding to the applied pneumatic pressure. The camera mounted directly in front of
the waveguide is used to capture the cross section of the levitation system. The camera is
zoomed into the levitation platform with sharp focus. A small ISO is chosen to minimise the
noise. An external light source was also added on the back of the structure to form Contre
Jour photo, which emphasizes the edges of each component, and software is used to calibrate
through a certain length on the graph, then measure the distance between edges pixels by
pixel. The results would be used to determine the position of the levitation platform relative
to the air floor.
Figure 4.4: Photographic processing for levitation measurement due to different pneumatic
pressure
Figure 4.4 shows photographs of the levitated platform on the left with 1300 Pascal static
pressure applied and the case of no applied pressure or levitation on the right. The lighter
areas in the pictures are the levitation platform and the air floor thanks to optical properties of
PMMA. The dark strip in the middle is the separation s between them, which is the result of
both initial separation (skirt height) and the levitation height caused by pneumatic pressure.
The difference in separation is the levitation height once the pneumatic force is introduced.
63
A collection of measurements is conducted using different pneumatic pressures/levitation
heights shown in Figure 4.5. The levitation platform is not lifted until about 300 Pa. Then as
the air pressure is increasing, the levitation height of the platform is growing. However, from
the experiments, the platform became unstable as the air pressure approaches the maximum
the pump offered.
Figure 4.5: Levitation height vs applied pneumatic pressure
According to fundamental physics, the pressure required to counter-balance the weight of an
object is equal to the gravity of the object. To lift the object, a force larger than the gravity of
the object needs to act on it to change its state and move it upwards. In this levitation system,
the platform is controlled by the pneumatic pressure continuously pumping into the system.
The increase of the total pressure leads to acceleration of the platform towards the opposite
direction of gravity leading to levitation. During the movement, the enlarged space under the
0 500 1000 1500 2000
0.00
0.05
0.10
0.15
0.20
0.25
Lev
ita
tio
n H
eig
ht
(mm
)
Pneumatic Pressure (pa)
64
levitation platform provides more space for pneumatic pressure to discharge. The platform
will reach to a balanced state once the total pressure acting on it is reduced to remain
identical to the gravity of the platform.
As shown in Figure 4.5, the pressure required for the levitation platform is noticeably larger
compared to previously measured levitation potential using an ordinary platform design.
That is because the open slots cut on the skirt provide additional paths for air to flow, which
generates rotational momentum. Therefore, the pneumatic pressure contributes to the lifting
force is dispersed. The smaller size of the levitation platform also enlarges the gap between
the confinement walls that impact the discharge of the airflow. The results shown in Figure
4.5 provide the levitation potential of the pneumatic structure for the new levitation platform.
Since the SRR is synchronized with the platform, the extra levitation height due to increasing
air pressure is reflected on the separation between broad-side coupled SRRs.
65
4.4 Split ring resonator design
The two identical SRRs used in this section in broad-side coupled formation are etched on a
Rogers RT/duroid 5880 substrate with relative permittivity εr = 2.2 and loss tangent tan δ =
0.0009 using conventional printed circuit board fabrication processes.
Figure 4.6: Schematic of the broad-side coupled SRRs: r = 6mm, w = 0.6 mm, g = 0.5 mm, R
= 7 mm, t = 0.508 mm, s = separation between two rings with initial 0.5 mm value due to h2
in Fig. 4.2(a), θ = ring rotation angle.
The separation and relative rotation angle shown in Figure. 4.6 are two major parameters that
change the interaction and control of the coupling of the broadside SRRs. The separation
between the two split rings is defined as the sum of the skirt height and the levitation height
extracted from Figure 4.5. The relative rotation angle is controllable by the positioning the
ridges on the bumper of the air floor.
66
4.5 Simulation and measurement
ANSYS HFSS is used to provide electromagnetic simulation. Figure 4.7 shows the
experiment setup used to measure the electromagnetic response of the SRRs controlled by the
pneumatic system. The whole structure is fitted into an additional segment of the WR-284
rectangular waveguide. The pneumatic input is delivered to the structure inside the
waveguide via a 2 mm hole on the bottom. Then air is exhausted through an array of small
holes in the waveguide located directly on top of the levitation structure. The inlet and
exhaust holes are examined both in the electromagnetic and aerodynamic environment to
ensure they do not disturb the system operation. The electromagnetic transmission results are
captured by an Agilent E5071B vector network analyzer.
Figure 4.7: Experimental set-up
67
Figure 4.8: Simulation model for examining the holes in the waveguide
The simulated electric field and the magnetic field is examined to compare the influence of
the open holes on the transmission properties of the rectangular waveguide. The copper
colored structure shown in Figure 4.8 is the waveguide segment under simulation. Multiple
non-modelled planes are placed across the structure in different orientations to monitor the
field distribution. The surface with colour gradient in Figure 4.8 is further demonstrated in
Figure 4.9, showing the magnetic field distribution on the cross section of the waveguide
along the propagation direction. Although scattering is observed around the edges of the
holes, the affected area is minor compared with the cross-section of the waveguide. The
central transmission where SRRs are located is unaffected.
The aerodynamic results mainly focus on determining whether the continuously pumped air
into the sealed waveguide is fully released through the top exhaust. It is expected that the air
68
trapped inside the waveguide would produce positive pressure onto the spinning platform,
causing extra friction and lowering the spinning speed. A measurement is carried out
comparing the spinning speed profile of the levitation platform with equal and minimum
pneumatic pressure in and out of the sealed waveguide. Sizes of the exhaust holes were
determined to be sufficient when no noticeable speed variation is observed.
(a)
(b)
Figure 4.9: Magnetic field distributions on the cross section of the waveguide along wave
propagation direction. (a) Field distribution on the conventional waveguide. (b) Field
distribution with holes on the waveguide.
69
(a) (b)
Figure 4.10: Electric field distribution of two broad-side coupled SRRs
(a) large separation (b) small separation
Changing the separation between the two SRRs is one of the key controlling parameters when
designing the structure in electromagnetic simulation. Theoretically, from the equivalent
circuit of broad-side coupled SRRs, the alteration of separation causes the mutual capacitance
to change. The electric field distribution plotted on a cross-section of a pair of broad-side
coupled SRRs in Figure 4.10 provides further insight into the coupling between the two SRRs.
The coupling strength in Figure 4.10(a) is much weaker than that of the SRRs with smaller
separation in Figure 4.10(b). As a strong coupling is desired for resonant frequency tuning
based on alteration of separation between two SRRs, it is necessary to attach the upper SRR
on the underside of the levitation platform.
To ensure the pneumatic structure itself does not significantly influence the resonant response
of the SRRs, the pneumatic structure is inserted into the simulation. The transmission result
is shown in Figure 4.11. Besides the downward slope coming from the cut-off frequency of
SRR1
SRR2
SRR1
SRR2
70
waveguide WR-284, there is no evident resonance observed in the frequency range of interest
up to 3.3 GHz.
Figure 4.11: Simulation result of the empty pneumatic structure in waveguide
4.6 Reconfiguration results
The electromagnetic transmission response of the coupled SRRs is simulated with different
separations s and relative rotational angles. The separation parameter s is the levitation
height plus the initial 0.5 mm separation between the levitation platform and the air floor
(skirt height t2 in Fig. 4.3(a)). The rotational angle ranges from 0˚ to 180˚ with a step of 45˚
are governed by the physical ridges located on the fabricated air floor bumper. Due to the
symmetrical design of the structure, the transmission response from 180˚ to 360˚ is the
inverse of the transmission from 0˚ to 180˚, and hence the results are not shown. Figure 4.12
represents half the rotation cycle of the upper split ring around its central axis without
levitation. As θ increases, the resonant frequency decreases up to 35% when θ = 180˚. The
reverse phenomenon occurs as θ continues to grow from 180˚ to 360˚. Very good
congruence between simulation and measurement is observed.
2.2 2.4 2.6 2.8 3.0 3.2-12
-10
-8
-6
-4
-2
0|S
21| (
dB
)
Frequency (GHz)
Pneumatic Structure
71
(a)
(b)
Figure 4.12: |S21| values of coupled SRRs at different rotation angle with s = 0.5mm
(a) Simulation results (b) Measurement
The transmission response corresponding to the separation s between the broadside coupled
SRRs is investigated in Figure 4.13. As described in Figure. 4.5, the levitation platform
requires a certain level of lifting pressure to bypass the bumper ridges, allowing the platform
to spin. This represents an upper limit for tuning the response utilizing the separation
variation, defined by the structural design.
2.1 2.4 2.7 3.0 3.3-21
-18
-15
-12
-9
-6
-3
0
Frequency (GHz)
|S21| (d
B)
0o
45o
90o
135o
180o
(a)
2.1 2.4 2.7 3.0 3.3-21
-18
-15
-12
-9
-6
-3
0
(b)
|S21| (d
B)
Frequency (GHz)
0o
45o
90o
135o
180o
72
The simulated transmission in Figure 4.13 indicates that increasing the space between SRRs
results in an elevated resonant frequency. The simulation shows the resonant frequency can
be shifted by a minimum of 0.7 % at θ = 0˚. The difference in the simulated and measured
results is caused by slight structural variations. Larger tuning is seen at other rotational
angles up to a value of 11.3 %, as shown in Figure 4.14 and summarised in Table 4.1. Hence,
pneumatic driven alteration of the separation between the coupled SRRs can provide one-
dimensional discrete tuning of the resonant frequency at all dedicated rotation angles
independently.
The drop of S21 magnitude of the measured results is mainly due to the lossy material
surrounding the coupled SRRs. Materials used are selected for accessible fabrication and
high visibility to inspect and demonstrate the operation of the structure. Materials with
improved electrical characteristics could easily be employed for a more practical structure.
(a) (b)
Figure 4.13: |S21| with different separation s when rotation angle is θ = 0o
(a) Simulated (b) Measured
3.10 3.15 3.20 3.25 3.30-18
-15
-12
-9
-6
-3
0
Frequency (GHz)
(a)
|S21| (d
B)
0.5 mm
0.55 mm
0.6 mm
0.65 mm
0.7 mm
3.10 3.15 3.20 3.25 3.30-18
-15
-12
-9
-6
-3
0
(b)
0.5 mm
0.55 mm
0.6 mm
0.65 mm
0.7 mm
|S21| (d
B)
Frequency (GHz)
73
Figure 4.14: Simulated/Measured results comparison at different rotation angles versus
separation (a)/(b) θ = 45o, (c)/(d) θ = 90o, (e)/(f) θ = 135o, (g)/(h) θ = 180o.
2.7 2.8 2.9 3.0 3.1-25
-20
-15
-10
-5
0
|S21| (d
B)
Frequency (GHz)
0.5 mm
0.55 mm
0.6 mm
0.65 mm
0.7 mm
2.7 2.8 2.9 3.0 3.1-25
-20
-15
-10
-5
0
|S21| (d
B)
Frequency (GHz)
0.5 mm
0.55 mm
0.6 mm
0.65 mm
0.7 mm
2.3 2.4 2.5 2.6 2.7-25
-20
-15
-10
-5
0
|S21| (d
B)
Frequency (GHz)
0.5 mm
0.55 mm
0.6 mm
0.65 mm
0.7 mm
2.3 2.4 2.5 2.6 2.7-25
-20
-15
-10
-5
0
|S21| (d
B)
Frequency (GHz)
0.5 mm
0.55 mm
0.6 mm
0.65 mm
0.7 mm
2.1 2.2 2.3 2.4 2.5 2.6-20
-15
-10
-5
0
|S21| (d
B)
Frequency (GHz)
0.5 mm
0.55 mm
0.6 mm
0.65 mm
0.7 mm
2.1 2.2 2.3 2.4 2.5 2.6-20
-15
-10
-5
0
|S21| (d
B)
Frequency (GHz)
0.5 mm
0.55 mm
0.6 mm
0.65 mm
0.7 mm
2.1 2.2 2.3 2.4 2.5-20
-15
-10
-5
0
|S21| (d
B)
Frequency (GHz)
0.5 mm
0.55 mm
0.6 mm
0.65 mm
0.7 mm
2.1 2.2 2.3 2.4 2.5-20
-15
-10
-5
0
|S21| (d
B)
Frequency (GHz)
0.5 mm
0.55 mm
0.6 mm
0.65 mm
0.7 mm
(a) (b)
(c) (d)
(e) (f)
(g) (h)
74
Table 4.1: Summary of the tuning range at different rotation angles.
Θ (o) 0 45 90 135 180
frequency tuning (%)
0.7 7.5 9.6 9.5 11.3
Figure 4.15: Control mapping of the broad-side coupled SRRs using the pneumatic switching
Both rotation angle and separation of broad-side coupled SRRs has the influence on the
resonant frequency to different extents. Figure 4.15 indicates the control mapping of the
combination of rotation angle and separation attributed to the resonant frequency shift. A
wide range of control is observed. The sharp steps on the control map come from the
phenomenon shown in Figure 4.12 that the resonant frequency shifts more drastically in
lower rotation angles due to a more obvious change in mutual capacitance.
0 5 10 15 20 252.0
2.5
3.0
3.5
Fre
qu
ency
(G
Hz)
Steps
Simulation
Measurement
75
4.7 Equalising frequency step
4.7.1 Structure alteration
Figure 4.15 highlights the extent to which the tuning phenomena can be exploited, depicting a
combination of simulation results at various values of s and θ. This underlines the potential
to achieve an extremely broad range of control over the resonant frequency. However, the
frequency shift is more significant when the rotation angle is smaller compared to angles
closer to 180˚, as observed in Figure 4.12. Consequently, some of the controlled states
overlap in the lower resonant frequency range, and gaps are evident at higher frequencies.
In order to make the frequency shift more even, the position of the ridges on air floor bumper
can be redesigned to accommodate for these irregularities. By analyzing the results of
resonant frequency over the rotational angle in the previous section, (2) can be applied to find
the corresponding resonant frequency at a dedicated rotation configuration.
𝑓 = 4𝑒−5𝜃2 − 0.0135𝜃 + 3.2513 (2)
where f = resonant frequency in GHz, θ = rotation angle of the top ring in degrees. Using
equation 2, the θ values of 0 o, 20 o, 40 o 80 o, and 180 o can be derived to obtain a more evenly
distributed frequency shift for s = 0.5 mm. Both air floor and levitation platform can be
removed from the confinement module and exchanged with a new pair with stopping ridge
positions at 0 o, 20 o, 40 o, 80o and 180o.
76
4.7.2 Results verification
Both simulations and measurements are conducted using the previously discussed processes.
Figure 4.16 indicates the frequency shift due to rotation angle is more evenly spread. Then
the results of the variations in s are shown in Figure 4.17.
Figure 4.16: |S21| tunability based on the angle θ between two rings when s = 0 mm for the
equalised frequency step structure (a) simulation (b) measurement
2.1 2.4 2.7 3.0 3.3-21
-18
-15
-12
-9
-6
-3
0
(b)
0o
20o
40o
80o
180o
|S21| (d
B)
Frequency (GHz)
-21
-18
-15
-12
-9
-6
-3
0
(a)
0o
20o
40o
80o
180o
|S21| (d
B)
3.10 3.15 3.20 3.25 3.30-18
-15
-12
-9
-6
-3
0
(b)
0 mm
0.05 mm
0.1 mm
0.15 mm
0.2 mm
|S21| (d
B)
Frequency (GHz)
-18
-15
-12
-9
-6
-3
0
(a)
|S21| (d
B)
0 mm
0.05 mm
0.1 mm
0.15 mm
0.2 mm-21
-18
-15
-12
-9
-6
-3
0
|S21| (d
B)
0o
45o
90o
135o
180o
(a)
2.1 2.4 2.7 3.0 3.3-21
-18
-15
-12
-9
-6
-3
0
(b)
|S21| (d
B)
Frequency (GHz)
0o
45o
90o
135o
180o
77
(a) (b)
(c) (d)
(e) (f)
3.10 3.15 3.20 3.25 3.30-18
-15
-12
-9
-6
-3
0
Frequency (GHz)
(a)
|S21| (d
B)
0.5 mm
0.55 mm
0.6 mm
0.65 mm
0.7 mm
3.10 3.15 3.20 3.25 3.30-18
-15
-12
-9
-6
-3
0
(b)
0.5 mm
0.55 mm
0.6 mm
0.65 mm
0.7 mm
|S21| (d
B)
Frequency (GHz)
3.00 3.05 3.10 3.15 3.20 3.25-25
-20
-15
-10
-5
0
|S21| (d
B)
Frequency (GHz)
0.5 mm
0.55 mm
0.6 mm
0.65 mm
0.7 mm
3.00 3.05 3.10 3.15 3.20 3.25 3.30-25
-20
-15
-10
-5
0|S
21| (d
B)
Frequency (GHz)
0.5 mm
0.55 mm
0.6 mm
0.65 mm
0.7 mm
2.7 2.8 2.9 3.0 3.1-25
-20
-15
-10
-5
0
|S21| (d
B)
Frequency (GHz)
0.5 mm
0.55 mm
0.6 mm
0.65 mm
0.7 mm
2.7 2.8 2.9 3.0 3.1-25
-20
-15
-10
-5
0
|S21| (d
B)
Frequency (GHz)
0.5 mm
0.55 mm
0.6 mm
0.65 mm
0.7 mm
78
(g) (h)
(i) (j)
Figure 4.17: Simulated/Measured |S21| comparison at different rotation angles versus
separation (a)/(b) θ = 0o, (c)/(d) θ = 20o, (e)/(f) θ = 40o, (g)/(h) θ = 80o, (i)/(j) θ = 180o
2.5 2.6 2.7 2.8 2.9-25
-20
-15
-10
-5
0|S
21| (d
B)
Frequency (GHz)
0.5 mm
0.55 mm
0.6 mm
0.65 mm
0.7 mm
2.4 2.5 2.6 2.7 2.8-25
-20
-15
-10
-5
0
|S21| (d
B)
Frequency (GHz)
0.5 mm
0.55 mm
0.6 mm
0.65 mm
0.7 mm
2.1 2.2 2.3 2.4 2.5-20
-15
-10
-5
0
|S21| (d
B)
Frequency (GHz)
0.5 mm
0.55 mm
0.6 mm
0.65 mm
0.7 mm
2.1 2.2 2.3 2.4 2.5-20
-15
-10
-5
0|S
21| (d
B)
Frequency (GHz)
0.5 mm
0.55 mm
0.6 mm
0.65 mm
0.7 mm
79
Figure 4.18: Control mapping of the broad-side coupled SRRs using the equalised frequency
step pneumatic switch
The control of rotation angle and separation reflected on resonant frequency is displayed in
Figure 4.18. Compared to the control mapping in Figure 4.15, each step in frequency control
is more fluent. Further control of the electromagnetic response can be achieved using the
pneumatic levitation system with more precise methods of air pressure control, an increase in
bumper ridge height to expand tuning range, and additional stopping angles on the bumper.
0 5 10 15 20 252.0
2.5
3.0
3.5
Fre
qu
ency
(G
Hz)
Steps
Simulation
Measurement
80
4.8 Summary
In this chapter, a novel pneumatic levitation system provides structure tuning of broad-side
coupled SRRs over a 35% frequency range. The pneumatic system is used to supply the
active force to elevate the upper SRR and provide variation in the separation between two
vertically coupled SRRs. Also, the pneumatic force enables the rotational momentum of the
top SRR, so that the orientation of the resonators system can be reconfigured. Each
configuration of separation or mutual orientation can be controlled independently, limited to
one degree of freedom or controlled concurrently to provide three-dimensional structure
modifications. Both simulations and measurements of the resonant frequency show a
substantial non-linear shift due to orientation changes over 180 degree of the top ring. A
smaller variation is observed due to the vertical position of the upper SRR.
The combination of two controls has also been demonstrated such that the resonant frequency
of a pair of broad-side coupled SRRs can be reconfigured to a great number of states across a
broad frequency band. The pneumatic levitation technique can also be tailored to produce a
more even frequency step between states. The implementation of such a system introduces a
new method of tuning SRRs, hence providing reconfigurability post-fabrication to
metamaterials or any communication devices employing SRRs.
81
CHAPTER 5
Lateral control of SRRs using pneumatics
5.1 Introduction
In the previous chapters, a pneumatic levitation system has been employed to provide
structural tunability of broad-side coupled SRRs. Resonant frequencies of the SRRs system
can be modified through orientation of SRRs, the separation between them, or both factors
simultaneously. The balanced pneumatic pressure, a core principle of the levitation system, is
particularly useful for mitigating inevitable human error in normal lithography fabrication
procedures where the switching component is manually aligned. Because the movement of
the SRR is restricted to one degree of freedom, the electromagnetic response is the outcome
of only the structural changes. Previously, the SRRs controlled by the pneumatic system
allowed reconfiguration by rotation in the azimuthal plane, and vertical separation between
two SRRs.
Figure 5.1: Flowchart showing the methodology of this work. Sections in orange are not
discussed in this chapter.
82
In this chapter, an innovative structural tuning technique solely utilizing pneumatic lateral
control of a SRR is investigated as depicted in Figure 5.1. The implementation enables
transition between two coupling modes of SRR, which is the result of their relative locations.
Furthermore, the coupled SRRs are integrated into the design of Coplanar Waveguide (CPW)
and a monopole antenna as a demonstration of reconfigurability.
5.2 Lateral control of SRRs
5.2.1 Operational concept
The lateral movement of a SRR provides the possibility to shift between broad-side coupled
and edge coupled mode as depicted in Figure 5.2. With SRR2 remaining stationary, SRR1
can slide from an edge-coupled arrangement (offset by a vertical spacing) to a position where
two rings are stacked in a broadside coupled fashion. An L-C circuit can be considered to
describe the electrical relation between two SRRs in edge-coupled mode. Figure 5.3(a) shows
the SRR gap is considered as a capacitor Cs, whereas the mutual capacitance Co into two
parts on each side of the gaps when the SRRs are oriented with the gaps facing each other.
The value of the mutual capacitance in this circuit is primarily determined by the distance
between two SRRs.
83
Figure 5.2: Conversion of coupling mode arrangement for SRRs
(a)
(b)
Figure 5.3: Edge-coupled SRRs (a) Configuration A, and L-C equivalent circuit (b)
Configuration B
84
When the two SRRs are in edge coupled mode, two configurations are defined based on the
relative orientation of each SRR, as depicted in Figure 5.3. Figure 5.3(a) and (b) describe the
condition when the gaps are adjacent or opposite each other in the edge-coupled mode. Both
configurations become identical in terms of transmission response when the SRRs are aligned
in broad-side coupled mode, and the electromagnetic wave excites the two rings
simultaneously. The effect of the transition from edge coupled to broad-side coupled mode is
different for each orientation. Considering configuration A of Figure 5.3(a), the gaps of the
two SRRs are initially close when edge coupled but gradually separate as the SRR1 slides
under the SRR2. For configuration B, the contrary happens where the gaps start with the
maximum distance between them and gradually reduce this distance during the transition.
The divergence of transition between two configurations leads to the concept of the sectional
coupling between the gaps of the SRRs. Due to the electrical charges accumulated on the
gap end, they are considered as electric dipoles. The coupling between two gaps can be
described as Coulomb interaction, which contributes to the effective capacitance of the
coupling system.
5.2.2 Pneumatic lateral control structure
The structure depicted in Figure 5.4 is explored to enable the lateral control of a SRR by
manipulation of pneumatic pressure. The pneumatic system can be dissembled into three
layers of the same length and width, L = 48 mm, and W = 34 mm respectively. The bottom
layer, which delivers the pneumatic pressure into the structure, works as a relay to absorb the
total pressure and evenly distribute it inside the chamber. The height of the bottom layer h3
is equal to 15 mm. The intermediate layer is a rigid sheet used as air restrictor with height h2
= 1.5875 mm (1/16 inch), the details of which will be explained in next section. It is intended
85
that the controlled SRR1 will levitate above the air restrictor. The top layer of the structure
is secured above the air restrictor to limit the active movement area of SRR1. The height h3
of the top layer is 2 mm. The width of this area w = 13.6 mm leaves 0.3 mm space for airflow
on each side of SRR1, which has a 13 mm substrate, preventing it from touching the side
walls of the movement track. The length l = 28 mm provides sufficient space for SRR1 to
move in a longitudinal direction for conversion between edge coupled and broad-side coupled
mode. SRR2 is secured in a stationary position inside the upper section of the channel with
the conductive ring facing down so that the back of the substrate aligns with the top surface.
(a)
(b)
Figure 5.4: The layout of the pneumatic levitation system. (a) The completely assembled
structure on the left and exploded view of the structure on the right. (b) Underside view of the
top layer.
86
Different to the previous chapters where the SRRs are limited with the synchronized
levitation platform to only rotate freely in azimuthal plane or elevation in space, lateral
movement requires the SRR to constantly break the stream of the air flow. The conveying
motion of the SRR brings noticeable drag to the system leading to abandoning of the
levitation platform. The challenge to design the new pneumatic system is to solve the
instability caused by lifting the much smaller weight of the object, which is the SRR substrate
itself, and still provide sufficient thrust to move it horizontally. All layers of the structures
are independently fabricated on an isel-CNC CPM 4030-Isel micro-miller using polymethyl
methacrylate (PMMA) material for easy machinability and high optical transparency.
The thrust force used to laterally shift SRR1 is generated through the channel mechanism
implemented on the underside of the top layer as shown in Figure 5.4(b). Air passing through
the air restrictor from the bottom layer is re-oriented to horizontal pressure via a carefully
located groove and three evenly spaced outlets cutting into the air channel. The triangular
shape of the cut outlets restricts the pneumatic pressure further to decrease its impact area and
increase its effective longitudinal distance. Thus, the horizontal thrust does not overly affect
the levitation force, while still providing effective thrust momentum even when SRR1 is at a
considerable distance from the outlets. The structure utilises gravitational force as the
restoring momentum, which can be adjustable by tilting the structure towards the horizontal
outlets. The thrust which is generated by the pumped pneumatic pressure acts against the
inclined gravity of the SRR. The larger the pneumatic pressure is, the further the SRR can be
pushed. This is also reversible, as the pneumatic pressure start to drop, the SRR can return to
its starting position due to insufficient thrust against gravity. However, a minimum
pneumatic pressure is necessary to maintain the levitation of SRR for minimal friction.
87
5.2.3 Air restrictor layer
Initially, the air restrictor layer was designed similar to the orifice plates used in the previous
chapters. The structure is depicted in Figure 5.5(a) where the orifices have 0.65 mm diameter,
are spaced at 1.3 mm and are drilled on 0.25 mm thick acetate.
(a)
(b)
Figure 5.5: (a) Orifice plate (b) Air flow simulation of the orifice plate
Two major issues are revealed during the prototype testing. First, bending of the layer caused
by an excessive amount of pressure pushing through the orifice plate distorts the air bed.
Though the pneumatic pressure used in this system is small (maximum 1800 Pa), the space of
the active area is limited, and the positive pressure builds up in the chamber and eventually
bends the thin air restrictor layer. This indeed can be easily fixed using a thicker material for
88
higher resilience. However, this leads to the second issue encountered: The naturally
occurring pressure gradients coming from the orifices are unavoidable. Figure 5.5(b) shows a
cross section of the pneumatic structure under an air flow simulation. The red colour
indicates the area with high levels of pneumatic pressure. Due to the layout and natural
discharge from the orifices, the pressure through them is higher in the centre and gradually
reduces its magnitude towards the outside. The resultant phenomena reflected in the
experiment exhibits trapping of the SRR between the orifice arrays. In other words, the
lateral movement is halted by the vertical pressure coming from the lines of orifices. This not
only reduces the smoothness of the conveying greatly, but also raises the pressure threshold
for the initial the movement of the SRR. The ultimate solution to ease the uneven pressure is
by creating more closely spaced orifices with smaller diameters. Hence, the air restrictor
layer must satisfy the following requirements:
1. Dielectric material for minimal electromagnetic interference.
2. Rigid material to prevent bending under pneumatic pressure.
3. Flat and smooth surface to reduce friction, as the SRR is initially in contact with it.
4. Small pore size and regular porosity for even pressure distribution.
5. Sufficient dimension to fit in with other components of the system.
Based on these requirements, the material selection for the air restrictor concluded on a
porous media made of ultra-high molecular weight (UHMW) polyethylene sheet
manufactured by GenPore. The diameter of the pores is 10 microns and the material is of 40-
50% pore density. The polyethylene sheet is 1/16 inch thick (1.57 mm) and 18 x 18 inch
wide (457 mm x 457 mm). The hydrophobic characteristics of the sheet also eliminate any
influence caused by moisture in the air. Conclusively, position trapping caused by the
pressure gradient from an orifice plate is significantly suppressed with the new porous media
owing to its much smaller and denser pores. However, as the porous media has smaller and
89
denser pores, the pneumatic pressure delivered to the channel used for thrust system is
insufficient to push the SRR as far as when using the orifice plate. To compensate the overall
air restriction across the entire porous media, a vacant slot is fabricated on air restrictor right
under the channel for the thrust system allowing the pneumatic pressure to reach the channel
unfiltered. Hence the pressure can be converted to provide enough thrust potential. This
provides a smooth and consistent conveying motion to the SRR, which can be verified via
experiment.
5.2.4 Coupled Split Ring Resonators
The proposed coupled SRRs consist of two circular SRRs etched on a square substrate made
of Roger RT/duroid 5880 with relative permittivity εr = 2.2 and loss tangent tan δ = 0.0009.
They stack in a way that metallic traces of the SRRs are facing each other. The
electromagnetic wave excitation is oriented as shown in Figure 5.6(a). The two SRRs are
made with identical dimensions and materials except for the geometrical size of the substrate
due to the placement of SRR in the pneumatic system.
The length L1 of the top SRR substrate is equal to 13.6 mm, which allows it to be fixed in the
conveying channel. The length of L2 is selected to be 13 mm, leaving 0.3 mm clearance on
each side of the bottom SRR to the channel walls. The thickness of the substrates is t = 0.508
mm, and the separation between two SRRs is s = 1 mm. The outer radius of the rings is 6
mm, with the SRR gap g = 0.5 mm and the width of the metallic trace w = 0.6 mm. Figure
5.6(b) depicts the transition of the two SRRs from edge-coupled mode to broad-side coupled
mode distinguished by the lateral distance d between origins of the two split rings.
90
(a)
(b)
Figure 5.6: (a) Schematic of the coupled SRRs (b) representation of the coupling mode
transition
5.2.5 Simulation
The electromagnetic simulation is conducted using ANSYS HFSS. The results aim to
provide a prediction of the electromagnetic response corresponding to the lateral movement
of SRR1. Based on the horizontal separation between the origins of two SRRs marked as d in
Figure 5.6(b), the analysis consists of 5 progressive stages. The coupled SRRs start from the
displacement where they are considered as in edge coupled mode (d = 14 mm). The second
stage is selected to be the moment that a quarter of the SRRs are overlapped (d = 10.55 mm).
91
Similarly, the third stage and the fourth stage represent the condition of half overlapped (d =
7 mm) and three-quarters overlapped (d = 3.5 mm). The final stage is where the SRR1 is
entirely covered to form broad-side coupling with the top static SRR2 (d = 0 mm).
(a)
(b)
Figure 5.7: Simulation results for coupled SRRs with different displacement
(a) configuration A (b) configuration B
2.2 2.4 2.6 2.8 3.0 3.2 3.4-30
-25
-20
-15
-10
-5
0|S
21| (d
B)
Frequency (GHz)
14mm
10.5mm
7mm
3.5mm
0mm
2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8-25
-20
-15
-10
-5
0
|S21| (d
B)
Frequency (GHz)
14mm
10.5mm
7mm
3.5mm
0mm
92
The two configurations of SRRs given in Figure 5.3 versus their relative displacement d have
been considered during the simulation process. The simulation results in Figure 5.7 prove the
hypothesis that the distance between the SRR gaps has an influence on the transmission
response. The resonant frequency of the coupled SRRs of both configurations is close when
they are edge coupled (d = 14 mm) and broad-side coupled (d = 0 mm). However, the
deviation in response appears during the transition process. The essential difference of
whether the gaps are getting further from each other (configuration A) or getting closer
together (configuration B) determines not only the magnitude of the transmission response,
but also the presence of a second resonance of the coupled SRRs in the considered band.
5.2.6 Experimental Set-up and Measurements
The experimental set-up is essentially identical to that used in previous chapters, as
demonstrated in Figure 5.8. The pneumatic pressure originates from an air pump via a large
tank to regulate it from pulsed to consistent output. The pneumatic structure resides inside a
specially crafted rectangular waveguide that allows the air to be delivered into the waveguide
as well as discharge from it to maintain a balanced atmosphere inside the sealed space. An
Agilent E5071B vector network analyser has been connected to the waveguide for
electromagnetic measurements. The pneumatic pressure is carefully controlled to locate the
SRR to the designated position, where the displacement of two SRRs gradually decreases
from the original value of 14 mm until their origins are at the same vertical axis.
93
Figure 5.8: Schematic of the experimental set-up
(a) (b)
Figure 5.9: Measurement of |S21| for coupled SRRs with different displacement
(a) configuration A (b) configuration B.
The results in Figure 5.9 shows that in the |S21| response for both configurations, the resonant
frequency drops as the two rings shift from edge coupled to broad-side coupled mode.
Configuration B encounters less Coulomb interaction between the dipole-like gaps of the
SRRs resulting in a second resonant frequency shown in analytical range. The congruence of
2.2 2.4 2.6 2.8 3.0 3.2 3.4-30
-25
-20
-15
-10
-5
0
|S21| (d
B)
Frequency (GHz)
14mm
10.5mm
7mm
3.5mm
0mm
2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8-25
-20
-15
-10
-5
0
|S21| (d
B)
Frequency (GHz)
14mm
10.5mm
7mm
3.5mm
0mm
94
the frequency shift due to horizontal placement of SRRs verifies the simulated results and
demonstrates the practical implementation of a pneumatic system for effective control of the
lateral position of the SRR. This creates the new opportunities to extend the reconfigurability
of SRRs, and allows more interesting electromagnetic responses to be explored. Two
examples will be examined in the following sections.
5.3 Reconfigurable CPW filter
5.3.1 Introduction
The geometry layout of CPWs places all conductive components on the same plane, atop a
dielectric material. CPWs loaded with SRRs has been introduced and explored in filtering
applications. They are usually made by fabricating the SRR on the back of a CPW substrate.
The negative effective permeability of the SRR in its natural small bandwidth provides sharp
frequency rejection, creating a fundamental SRR loaded CPW filter.
The issue when designing the CPW filters with SRR is the native narrow band. The most
common approach to improve its bandwidth is by placing multiple adjoining SRRs with
slightly different performance. The contiguous frequency rejection due to each SRR is
combined to provide wider or multiple filtering bands. The common problem of the
combination of various resonators is the coupling between each resonators leading to
insertion loss. The statically etched SRRs on CPW also impede reconfiguration potential.
Based on the results demonstrated previously in this chapter, pneumatic controlled SRRs can
be an effective solution to design a reconfigurable CPW filter.
95
5.3.2 Structure and Simulation
In previous sections of this chapter, a pneumatic system has been explored and proven to be
an effective approach to providing lateral control of a SRR. The horizontal movement of the
SRR can be utilised in the design of a CPW filter. The implementation of the pneumatic
system with the CPW can be conducted by simply stacking the CPW perpendicularly on top
of the pneumatic structure of Figure 5.4 (replacing SRR2) with the conductors facing down.
The CPW used is shown in Figure 5.10.
Figure 5.10: Photograph of CPW: W1 = 14 mm, W2 = 3 mm, g0 =0 mm, L1 = 50 mm
With the replacement of the SRR2 with the CPW, SRR1 is located 1.5 mm below the CPW.
Based on the separation between the origin of the SRR and the centre of the transmission line,
marked as d in Figure 5.11, the performance of the CPW filter can be reconfigured
dynamically. For convenient demonstration purposes, the SRR is illustrated above the CPW
in Figure 5.11.
96
Figure 5.11 Diagram of the movement of the SRR relative to the CPW, distinguished by
separation d
The initial location of the SRR coincides with the centre of the transmission line. As the
pneumatic pressure increases, the second stage is reached where the SRR moves to d = 3 mm.
The system reaches its third stage when the gap of the SRR meets the gap between the central
line of the CPW and the lower ground plane (d = 6 mm). At d = 7.5 mm the gap moves to the
centre of the CPW line, and further displacements of d = 9 and 12 mm are examined.
Simulation is conducted using ANSYS HFSS to provide the theoretical expectation of the
filter. The different stages distinguished by the displacement of the SRR are shown in Figure
5.12.
Figure 5.12: Simulated |S21| of CPW filter using pneumatic controlled SRR.
2.8 3.0 3.2 3.4 3.6 3.8 4.0-16
-12
-8
-4
0
|S21| (d
B)
Frequency (GHz)
0mm
3mm
6mm
7.5mm
9mm
12mm
97
According to the simulation results, the band-stop response of the CPW filter is closely
related to the location of the nearby SRR. The frequency increases as the SRR moves along
its track. The strongest resonance is reached when the gap of the SRR overlaps with the CPW
gap. The changes in the magnitude of frequency rejection indicate the strong dependence of
relative location of the SRR and CPW gaps and the resulting coupling strength. It is also
evident that the resonance fades when the SRR is completely above the ground plane.
5.3.3 Measurement
Measurement is conducted by using similar setup mentioned in previous chapters, except a
rectangular waveguide is not required. The network analyser is directly connected to the two
ports of the CPW as shown in Figure 5.13, which is then stacked above the pneumatic
structure with conductors facing down. The pneumatic force is fed through the pipe under
the bottom layer of the pneumatic structure. The platform where the pneumatic structure is
held provides the necessary level for the operation, removing the negative influence caused
by a declining bench or floor. The change of transmission response is observed as the
pneumatic pressure is increased.
98
Figure 5.13: Experimental set-up
The six different stages of the CPW determined by the location of the SRR relative to the
centre of CPW are examined and depicted in Figure 5.14. Compared to the theoretical
simulation, the measurement presents similar frequency shift and magnitude variations due to
the horizontal placement of the SRR. The strongest band-stop frequency happens when the
SRR moves 6 mm from its origin position at 3.5 GHz. This is due to the maximum excitation
of the SRR when the gap is over the gap of the CPW. The vertical separation between the
SRR and the CPW is believed to cause the deviation of the experimentally determined
resonance from the theoretically predicted value.
99
Figure 5.14: Measured |S21| of CPW using pneumatic controlled SRR
An investigation of the field strength between the SRR and the CPW can provide valuable
information about the internal interaction. To observe the coupled system, the electric field
strength is plotted on the cross section of the SRR loaded CPW. Figure 5.15 shows two
distributions of the electric field with different separations between the CPW and the SRR.
The maximum electric field is induced at the gap of the CPW, which is adjacent to the gap of
the SRR. When the space between them is larger like in Figure 5.15 (a), the coupling
between the CPW and SRR is significantly weakened compared Figure 5.15 (b) which is 0.5
mm closer. Thus, the difference in coupling strength that is determined by the relative
location of CPW and SRR is responsible for the variation in the magnitude and frequency of
the simulated and measured results.
2.8 3.0 3.2 3.4 3.6 3.8 4.0-16
-12
-8
-4
0
|S21| (d
B)
Frequency (GHz)
0mm
3mm
6mm
7.5mm
9mm
12mm
100
(a) (b)
Figure 5.15: The field strength on the cross section of the CPW showing the coupling
between SRR and CPW. (a) electric field distribution with 1.5 mm separation between SRRs,
(b) electric field distribution with 1 mm separation between SRRs
5.3.4 Coupled SRRs loaded CPW filter
The addition of a SRR in proximity to a CPW can create a band-stop filtering effect, and the
operational band can be adjusted by moving the relative location of the SRR to the CPW via
the pneumatic system. To improve the performance of the SRR loaded CPW further, the
coupled SRRs analyzed in Section 5.2 are considered.
The incorporation of the CPW with coupled SRRs only requires laying the former over the
structure described in Figure 5.4 with the conductive section face down on the top surface of
the pneumatic structure. Figure 5.16 represents the operation of the reconfigurable filter. It
should be noted that the position of the CPW (orange color) is moved to the back for
clarification of the location of the SRRs. It has already been observed that the performance
of the band-stop filtering reaches its maxima when the gap of the SRR matches the lower gap
Gap on
CPW
Ground
Plane
Centre
conductor
SRR
101
of the CPW. Hence the location of the CPW is defined to match the gap of SRR2, yielding a
value of p = 6 mm.
Figure 5.16: Diagram of operation for the coupled SRRs loaded CPW filter.
The incorporation of CPW with the pneumatic system makes the CPW physically touch the
substrate of SRR2. While SRR2 remains static with its origin 6 mm away from the centre of
the transmission line, the SRR1 is controlled by pneumatic pressure and free to move in the
direction shown in Figure 5.16. Five stages are determined the same way as Section 5.2, and
d is used to indicate the distance between the origins of two SRRs.
(a) (b)
Figure 5.17: Simulation results with different distance d between the two SRRs
(a) configuration A (b) configuration B
2.6 2.8 3.0 3.2-20
-16
-12
-8
-4
0
|S21| (d
B)
Frequency (GHz)
14mm
10.5mm
7mm
3.5mm
0mm
2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0
-24
-20
-16
-12
-8
-4
0
|S21| (d
B)
Frequency (GHz)
14mm
10.5mm
7mm
3.5mm
0mm
102
The performance of the filter is simulated to provide the transmission coefficient of the CPW.
The results are shown in Figure 5.17 (a). When the two SRRs are in edge coupled mode, or
its separation is maximum at 14 mm, the resonant frequency is at 3.1 GHz. The merging of
the two SRRs causes the resonant frequency of the system to drop eventually to 2.66 GHz
once two SRRs coincide. The same analysis is undertaken when the configuration B is
considered. The simulation results are shown in Figure 5.17 (b), and as discussed before, the
influence of the dipole interaction between gaps of the two SRRs is minor, the second
resonance is closer and the resulting shift of the frequency is in the opposite direction once
the bottom SRR starts to move from edge coupled to broad-side coupled mode.
5.3.5 Measurement
Figure 5.18 shows the measured transmission response for both configuration A and B. In
configuration A, the filter resonates at 3.09 GHz when the SRRs are in edge-coupled mode.
The conversion to broad-side coupled mode drops it to 2.67 GHz. In configuration B, the
same frequency divide is observed. The filter with edge-coupled SRRs resonates at 3.15 GHz
and divides to 2.29 GHz and 3.85 GHz when broad-side coupled. The congruence of the
theoretical simulation and practical measurement proves the concept of a reconfigurable
coupled SRR loaded CPW filter, made possible by utilizing lateral control via a pneumatic
system.
103
(a) (b)
Figure 5.18: |S21| of CPW filter with different distance d between two SRRs
(a) configuration A (b) configuration B
5.4 Reconfigurable Antenna using SRRs
5.4.1 Introduction
SRRs have also been integrated into the design of reconfigurable antennas. Conventional
methods require the SRR to be etched in proximity to the antennas. The size, orientation, and
shape of the SRR have been explored to affect the operational performance of the antenna.
However, the physical integration of a SRR on antennas means the characteristics of the
antenna are fixed. In this section, the concept of dynamically moving a SRR horizontally
using pneumatic systems is considered to realise a reconfigurable antenna.
2.6 2.8 3.0 3.2-20
-16
-12
-8
-4
0|S
21| (d
B)
Frequency (GHz)
14mm
10.5mm
7mm
3.5mm
0mm
2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0-25
-20
-15
-10
-5
0
|S21| (d
B)
Frequency (GHz)
14mm
10.5mm
7mm
3.5mm
0mm
104
5.4.2 Structure and Simulation
The CPW-fed monopole antenna has advantages of a planar structure and omnidirectional
radiation. The CPW-fed monopole antenna used in this section is inspired by [74]. The
structure is altered and rescaled to replace the edge -coupled DSRR with broad-side coupled
SRRs as shown in Figure 5.19. The CPW is designed for 50 Ω characteristic impedance on
an FR-4 substrate with relative permittivity εr = 4.4, loss tangent tan δ = 0.02 and 0.8 mm
thickness. Two ground planes are placed symmetrically on each side of the central line. The
width and length of the ground planes are W1 = 14 mm, L1 = 26.5 mm respectively. Each
ground is g0 = 0.3mm away from the centre conductor for achieving 50 Ω. The length of the
centre conductor is extended by L2 = 3 mm and connected to a SRR to form a monopole
antenna. The size of the SRR attached to the feed line determines the operation frequency of
the antenna. The parameters of the SRR are: R = 6 mm, w = 0.6 mm, g = 0.5 mm. Another
SRR with identical geometry but etched on a 0.508 mm thick Roger RT/duriod 5880
substrate with relative permittivity εr = 2.2 and loss tangent tan δ = 0.0009 is located under
the antenna. The gap of the SRR is inverted to face in the opposite direction to the one on the
antenna.
105
Figure 5.19: Schematic of the CPW-fed monopole antenna tuned by a SRR.
As the pneumatic system proposed in this chapter can support the lateral control of the SRR,
the bottom SRR is designed to move in x direction on the x-y plane. The lateral separation s
between the SRR on the antenna and the pneumatically supported SRR is determined based
on the location of the origins. The movement direction of the SRR is defined as +x or –x
from the centre origin of the antenna SRR. The vertical space between two SRRs is fixed at
1.5 mm. Simulations are prepared via ANSYS HFSS using the ideal model of the CPW-fed
monopole antenna and SRR supported in air. The simulated results are shown in Figure 5.20.
106
(a)
(b)
Figure 5.20: Simulation results of the reconfigurable CPW-fed monopole antenna (a) |S11| (b)
radiation pattern in z-y and z- x plane without structure reconfiguration.
3.0 3.2 3.4 3.6 3.8 4.0-40
-30
-20
-10
0
|S11| (d
B)
Frequency (GHz)
s = 0 mm
s = -3 mm
s = 3 mm
s = -6 mm
s = 6 mm
0
30
60
90
120
150
180
210
240
270
300
330
-40
-30
-20
-10
0
-40
-30
-20
-10
0
z-y plane
z-x plane
107
The results in Figure 5.20(a) indicate that the operational frequency of the monopole antenna
is 3.64 GHz when the SRR moves directly underneath it (s = 0 mm). Lateral movement of
the SRR gradually splits the antenna operation into two bands, which space further apart for
larger s. The direction SRR movement (+/-x) does not have a noticeable effect on the |S11|
response of the system. A detailed list of the frequency band centres with respect to s is
given in Table 5.1.
Table 5.1: Frequency bands of the CPW-fed monopole antenna with different s
s in (mm) 0 -3 3 -6 6
Lower freq.
(GHz)
3.64
3.5 3.5 3.17 3.16
Higher freq.
(GHz)
3.77 3.77 3.84 3.82
Though the direction of which the SRR is moving does not significantly change the |S11|
response of the antenna, the physical arrangement of the antenna is reverse in both directions.
Therefore, a change in radiation pattern in the x-y plane due to the movement of the SRR is
expected. The radiation pattern and surface current distribution shown in Figure 5.21
confirms the symmetric structure of the system resulting typical donut-shape omnidirectional
radiation pattern in x- y plane when s = 0.
Figure 5.21: Radiation pattern in x-y plane at 3.64 GHz with s = 0 mm.
108
(a) (b)
(c) (d)
Figure 5.22: Radiation pattern and surface current distribution at: (a) 3.5 GHz, s = -3 mm, (b)
3.5 GHz, s = 3 mm, (c) 3.77 GHz s = -3 mm, (d) 3.77 GHz s = 3 mm
Figure 5.22 demonstrates the radiation pattern and surface current distributions when the
SRR is 3 mm away from the centre in the two opposite x-directions. The highest current is
generated around the gap of the SRR at a lower frequency, which distinguishes the radiation
pattern in two opposite locations of the SRR (Figure 5.22(a) and (b)). However, in Figure
5.22 (c) and (d), the opposite phenomena is observed at the higher frequency. This is caused
by the opposite direction of the current on the SRR resulting in a reversed radiation pattern.
The same phenomena are also observed when s = ± 6 mm, with a further tilt to the radiation
pattern. Hence a reconfigurable pattern tilt is observed with lateral movement of the SRR.
Bottom SRR
109
The radiation patterns of all configurations at their associated resonant frequencies is
provided in the polar graph shown in Figure 5.23.
(a)
(b)
Figure 5.23: Radiation pattern in different values of s (mm)
(a) at the lower resonant frequency (b) at the higher resonant frequency.
0
30
60
90
120
150
180
210
240
270
300
330
-50
-40
-30
-20
-10
0
-50
-40
-30
-20
-10
0
s = 0
s = -3
s = 3
s = -6
s = 6
0
30
60
90
120
150
180
210
240
270
300
330
-50
-40
-30
-20
-10
0
-50
-40
-30
-20
-10
0
s = 0
s = -3
s = 3
s = -6
s = 6
110
Further investigation of the reconfigurable radiation pattern utilizing the lateral movement of
the SRR is undertaken to observe the resultant radiation pattern at a static operational
frequency. A pattern frequency of 3.64 GHz was selected(resonant frequency of the
concentric SRR geometry) regardless of the position of the movable SRR. The radiation
patterns of different s of the SRR are presented in Figure 5.24 for this case.
Figure 5.24: Radiation pattern at 3.64 GHz
The results demonstrated in Figure 5.24 provide a similar tilting effect to the radiation pattern,
except the direction of the tilting is reversed when the SRR moves from s = -3 to -6 or from 3
to 6. As shown in Figure 5.20(a), the selected operational frequency is located on the upslope
of the first resonance for s = ± 3 mm, but on the downslope of the second resonance for s = ±
6 mm. This ultimately defines the corresponding mode of the SRR, resulting in opposite
direction of radiation pattern tilting for movement in the same direction.
The tilt of the radiation pattern of the proposed monopole antenna is reconfigurable in the x-y
plane with dynamic moving SRR in the x direction. It proves the concept of lateral
movement of SRR using pneumatic systems has the potential not just to tune the resonant
0
30
60
90
120
150
180
210
240
270
300
330
-50
-40
-30
-20
-10
0
-50
-40
-30
-20
-10
0
s = 0
s = -3
s = 3
s = -6
s = 6
111
frequency, but also the radiation pattern. The manipulation of the pneumatic controlled SRR
can be used to tilt the radiation pattern of a monopole antenna by either adjusting the
operational frequency or the direction of the movable SRR.
5.4.3 Experimental results
The verification of the results is conducted using the measurement of reflection coefficient
via a network analyser. The results are shown in Figure 5.25. The changes to the |S11| with s
match well with the simulations.
Figure 5.25: |S11| parameter of a monopole antenna with different placement of SRR.
The radiation pattern is evaluated inside an anechoic chamber at corresponding values of s
and operational frequencies, and the results are displayed in Figure 5.26. The changes to the
radiation pattern are observed coincide with the simulations. The radiation pattern is tilted
towards the direction of SRR at the lower resonant frequency band, but opposite at the higher
frequency band.
3.0 3.2 3.4 3.6 3.8 4.0-50
-40
-30
-20
-10
0
|S11| (d
B)
Frequency (GHz)
s = 0 mm
s = -3 mm
s = 3 mm
s = -6 mm
s = 6 mm
112
(a)
(b)
Figure 5.26: Measured Radiation pattern at a different s with associated frequency.
0
30
60
90
120
150
180
210
240
270
300
330
-50
-40
-30
-20
-10
0
-50
-40
-30
-20
-10
0
s = 0
s = -3
s = 3
s = -6
s = 6
0
30
60
90
120
150
180
210
240
270
300
330
-50
-40
-30
-20
-10
0
-50
-40
-30
-20
-10
0
s = 0
s = -3
s = 3
s = -6
s = 6
113
Figure 5.27: Radiation pattern at fixed frequency (3.5 GHz)
The same procedure is used to measure the radiation pattern at a fixed operational frequency.
The operational frequency fixed at 3.5 GHz is located within the lower resonant band when s
= ±3 mm and the upper resonant band when s = ±6 mm. As expected, the changes to the
radiation pattern favored the corresponding mode of SRR, resulting in opposite direction of
radiation pattern when advancing the SRR in one direction.
0
30
60
90
120
150
180
210
240
270
300
330
-50
-40
-30
-20
-10
0
-50
-40
-30
-20
-10
0
s = 0
s = -3
s = 3
s = -6
s = 6
114
5.5 Summary
This chapter broadens the reconfigurability of a SRR by introducing lateral control realised
by a pneumatic system. The smooth conveying motion provided by the pneumatic structure
in the horizontal plane can be used to shift a pair of SRRs between edge-coupled to broad-
side coupled mode. Both simulation and measurement demonstrate the influence on the
resonant frequency due to the lateral separation between SRRs. Depending on the initial
orientation of the SRRs, the frequency is shown to change by 28% from around 3.2 GHz, and
second resonance may appear to change in the opposite direction. Further investigation and
validation of the pneumatic lateral movement of a SRR are undertaken by integrating it into
the design of CPW filter and monopole antenna. The lateral arrangement of the SRR
supported by the pneumatic structure has been shown to be a novel and effective approach to
explore the reconfiguration of SRRs.
115
CHAPTER 6
Thesis Summary
6.1 Introduction
This primary aim of this thesis is to investigate the reconfigurability of SRRs utilizing
pneumatic levitation techniques. The structural arrangement of single and coupled SRR
systems can be reconfigured by the incorporation of the pneumatic control system. By
adjusting the level of the input pneumatic pressure, the orientation, vertical placement or
horizontal location of the SRR can be tailored to achieve a desirable transmission response.
The introduction of pneumatic system minimise the interference caused by conventional
metallic components and bias structures, reduce alignment error thanks to the aerodynamics,
and extend the operation time due to its contactless characteristics. A summary of this thesis
is provided in the following sections based on the outcomes of each chapter.
6.2 Chapter 1 and 2
The rapid development of communication systems demands that RF devices operate in a
variety of conditions, both system based and environmental. The investigation of SRRs,
which is essentially a small L-C resonant circuit, provides opportunity to customise and
enhance the performance of the SRR loaded RF devices due to its sharp response, compact
size and ease of modification. However, the SRR is usually narrow-band, which adds
restriction to how much a SRR loaded system can be improved. The simple approach to
solving this issue is to enable reconfiguration of the SRR. A comprehensive study of the
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existing methods for reconfiguring SRRs was undertaken to reveal the issues with current
reconfigurable SRRs. The motivation of the thesis to explore pneumatically controlled SRR
is addressed. The objectives of this research include investigating and evaluating various
pneumatic levitation systems to garner specific electromagnetic responses, the influence of
the varying the arrangement of an SRR in different dimensions on the transmission response,
and the incorporation of the pneumatic controlled SRR system with fundamental RF devices.
6.2 Chapter 3
Background: The implementation of a SRR in RF devices has seen rapid expansion due to
the discovery of the metamaterials. The properties of an individual SRR have been
extensively studied in the literature, including parameter analysis and field orientation. The
orientation of a single SRR in the electromagnetic field has the influence on the transmission
response. This phenomenon has also been investigated using broad-side coupled SRRs,
which consist of two identical SRRs stacked along a central axis. Based on the fact that the
change of orientation results in frequency shift, several methods have been studied to enable
such a configuration change, such as MEMS switches, mechanical force, and fluidic channels.
The outcomes have shown reconfigurability that serves to improve the performance of the
naturally narrow bandwidth of the SRR.
However, these conventional methods often bring unavoidable electromagnetic interference
caused by the extra electric components and actuation networks, misalignment due to the
fabrication processes, and unreliable mechanical movement that leads to unpredictable
degrees of freedom. These issues significantly obstruct the development of SRRs for highly
efficient and flexible application. The introduction of a pneumatic system intends to
117
minimise the interference and provide a counterbalance to the system so that the actuation is
limited to the dependent variable.
Aim of the research: To investigate and realise a pneumatic levitation system to allow a
continuous orientation change of a SRR in an incident field in order to achieve a swept
frequency response.
Methodology: The study of SRRs and coupled SRRs provided the background knowledge
for orientation reconfiguration for this investigation. The pneumatic levitation system is
inspired by a hovercraft, air hockey pucks, and air bearings. For stable levitation and smooth
rotation, its geometrical structure was examined using ANSYS fluid simulation. ANSYS
HFSS was used to theoretically simulate the expected dynamic shift of transmission response
due to orientation spinning of the SRR. The simulation results were validated through
measurement in a rectangular waveguide.
Results: The pneumatic levitation system has shown control over the spinning speed and
hence frequency sweep response rate of individual SRR and coupled SRR systems. Both
simulation and measurement show that the spinning motion of single SRR results in 0.3% of
frequency sweep twice in one revolution. The swept frequency range is substantially
enlarged by using broad-side coupled SRRs, with one ring statically located below the
continuously spinning SRR. Results exhibited a 12% frequency sweep between 2.33 GHz
and 2.65 GHz, and 10% frequency sweep between 2.39 GHz and 2.66 GHz corresponding to
the perpendicular and parallel placement of the static SRR relative to E-field respectively.
The design of the interchangeable levitation platform that holds the SRR is also examined to
demonstrate distinct spinning speed profiles for extended customization of reconfigurable
SRRs.
118
Future Work: The continuous spinning of the SRR orientation in the incident field provides
a frequency sweep over a large frequency band. Incorporating the pneumatic levitation
controlled SRR system into a sensor or radar system would provide a dynamic tuning
technique without electromagnetic interference. A future advance to the aerodynamic design
of the levitation platform may allow for self-acting levitation and spinning, which could
remove the need for the pneumatic source during operation.
Original Contribution: A pneumatic levitation system investigated that exhibits dynamic
frequency reconfigurability of SRRs due to the change of orientation, providing a novel
technique to enable reconfigurable resonant RF devices and structures that eliminate the
interference from metallic bias lines.
6.3 Chapter 4
Background: Both the orientation and separation of broadside-coupled SRRs, as determined
by their structural arrangement, have been shown to influence their resonant frequency.
Recent studies have demonstrated several approaches to achieve frequency reconfigurability
utilizing the structural tuning of SRRs, yet each have their drawbacks. In Chapter 3, a new
method to change the static orientation of SRRs in a controlled manner using pneumatic
levitation is investigated, alleviating the problems in conventional reconfiguration methods.
In addition, the separation of broad-side coupled SRRs defined by their vertical structural
arrangement plays an important role to determine the resonant frequency. According to the
levitation verification in Chapter 3, it is also possible to realise separation tuning of broad-
side coupled SRR using the pneumatic system.
119
Aim of the research: To enable precise control over the static orientation and separation of
SRRs using a pneumatic levitation system, in order to observe discrete frequency
reconfiguration.
Methodology: Based on the structure used in Chapter 3, which successfully demonstrated the
continuous rotation of orientation, an extra mechanism was implemented to stop the spinning
motion at the desired rotational angle(s). Thus a specific resonant frequency response from
broadside-coupled SRRs can be achieved by controlling the pneumatic pressure. Both fluid
and electromagnetic simulation are used to provide the guidelines for fabrication of
pneumatic structure and expected transmission response. Experiments in a rectangular
waveguide were conducted to validate the hypothesis.
Results: Broad-side coupled SRRs are shown to be reconfigurable using pneumatic levitation
system with 35% of frequency tuning range observed. In an initial demonstration, the
stopping mechanisms on the pneumatic structure allow the levitated SRR to stop at every 45o
for discrete selection of the resonant frequency. Also, the separation between the two
coupled SRRs is controllable by using different levels of pneumatic pressure ranging from
300 Pa to 1800 Pa. Depending on the orientation of the top SRR, the frequency tuning range
due to separation can vary between 0.7% and 11.3%, with 0o orientation being the lowest and
180o being the highest. The discrete control on both the orientation and separation of SRRs
unlocks the advanced potential for reconfigurable resonators by realising a series of dedicated
resonant frequencies over a large band. The structure is also proven to be customisable based
on the stopping mechanism design, with an altered arrangement of stopping angles providing
an even frequency step.
120
Future Work: The new pneumatic levitation system has shown precise control of the
resonant frequency of broadside-coupled SRRs utilizing structural alteration to their relative
orientation and separation. The selection of the resonant frequency is based on both the
rotational angle determined by the stopping mechanisms and the applied pneumatic pressure.
Each distinct stage is limited by how close the designed stopping points can be and how fine
the control of the pneumatic pressure. The micro-miller used to fabricate the structure is
accurate enough to provide physical placement of the stopping point at the current scale.
Micro fabrication methods could be explored to implement such systems at a higher
frequency range. Also, the analog pneumatic pump has an insufficient response time and
large increment step, so implementing a digital pneumatic pump or even a microfluidic
control array could be used to provide more control on the selection of frequency.
Original Contribution: A dedicated frequency selection pneumatic system based on the
rotational angle and vertical separation of broadside-coupled SRRs is realised. The
combination of orientation and separation of the SRRs controlled by pneumatic levitation
system presents an array of discrete frequency reconfiguration that can be tailored depending
on operational requirements.
6.4 Chapter 5
Background: Chapter 3 and Chapter 4 have proposed and demonstrated the incorporation of
pneumatic levitation systems into fundamental broad-side coupled SRR structures. The
outcomes highlight the frequency reconfiguration due to the structural arrangement of the
resonators in the azimuthal rotation and vertical separation. The literature review suggests
that coupled SRRs can also be placed in the same plane to form edge coupled SRRs. Both
121
edge coupled and broad-side coupled modes have been explored independently, and their
performance differences and implications have been discussed. Although several approaches
have been proposed to alter the structure to each mode, there has not been an efficient method
to convert them dynamically. Pneumatic systems reduce the friction caused by physical
movement whilst requiring no electric component or bias structures that can interfere with
electromagnetic performance. Hence they are proposed as a solution to physically switch
coupled SRRs between the two coupling modes. The resonant frequency of the coupled SRR
is expected to be adjustable during this process.
Aim of the research: To explore the potential of a pneumatic system to allow lateral control
over the arrangement of the coupled SRRs or SRR systems. Also, to incorporate the
reconfigurable SRR system with fundamental RF devices prototypes to achieve
pneumatically adjustable operation.
Methodology: Achieving different coupling modes based on the relative location of the
SRRs is based on the equivalent L-C circuit, which the mutual capacitance is determined by
the distance between conductive elements of the SRRs. With an upper SRR fixed in position,
lower SRR can be driven by pneumatic force to adjust along one dimension the relative
arrangement of the two split rings. To achieve the lateral control of the SRR, a pneumatic
levitation structure is investigated to encounter less drag during the conveying movement.
Determination of the optimal size of the conveying track for contactless operation and
selection of the porous media for best distribution of lifting momentum are critical research
steps. Electromagnetic simulation is undertaken in ANSYS HFSS to predict the transmission
response due to the change in the arrangement and coupling mode of the SRRs. The results
are validated via experiment. A tunable CPW filter element and monopole antenna are
devised and fabricated to demonstrate the reconfiguration capability by lateral control of
coupled SRRs using the pneumatic levitation system.
122
Results: The modification to the horizontal arrangement of the SRR is enabled by pneumatic
force is converted to thrust, while the consistent levitation ensures the minimum friction. The
resonant frequency related to the lateral separation between two coupled SRR shows 28%
frequency variation from 3.2 GHz to 2.3 GHz during the transition from edge-coupled to
broad-side coupled mode. A second resonance appears when the gaps of the SRR are facing
outward in the initial edge-coupled arrangement, which has a resulting frequency shift in the
opposite direction.
The implementation of a single laterally controlled SRR into the design of a CPW
demonstrates a tunable band-stop frequency, which is adjustable by horizontal placement of
the SRR using the pneumatic system. The addition of another SRR to form coupled
resonators improves the tunable range. The tunable range of the frequency rejection band
was 15% for the fundamental resonance.
Both operational frequency and radiation pattern of CPW fed monopole antenna have been
reconfigured using the lateral movement of a SRR. Moving the SRR in the horizontal plane
splits the operational frequency of the antenna analogous to the dual mode of a SRR. The
resulting radiation pattern is tilted, and the tilt can be controlled by tailoring the position of
the current maxima and current direction, the operational frequency, and/or the lateral
position of the SRR.
Future Work: The recent investigations into the near-field interaction between SRRs found
that mechanical force is generated due to Lorentz force when exciting with a strong
electromagnetic wave. This can be utilised to explore self-acting nonlinear control in a
lateral plane without the requirement for thrust converted from the pneumatic input. The
challenge lays in the balance between the strength of the induced mechanical force and
friction reduction using pneumatic levitation.
123
Original Contribution: The lateral arrangement of the SRR is reconfigured using the
pneumatic system. The conveying movement provided to a SRR can smoothly transfer it
between edge-coupled and broad-side coupled mode. The resulting variation to lateral
separation has shown reconfiguration in frequency. With integration to a CPW and antenna,
the lateral control of the SRR realised by a pneumatic levitation system has provided efficient
reconfiguration of filtering characteristics, impedance bandwidth and radiation pattern.
124
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